quickfur wrote:What would be really cool, is a projection or slice of a 6D (or higher) toratope that produces icosahedral symmetry.
Or better yet, a slice of an 8D toratope that produces 600-cell symmetry (though we'd have a hard time recognizing that in the 3D slices!).
2D : (II)
3D : ((II)I)
4D : ((II)(II)) (((II)I)I)
5D : (((II)I)(II)) (((II)(II))I) ((((II)I)I)I)
6D : (((II)I)((II)I)) ((((II)I)(II))I) ((((II)(II))I)I) (((((II)I)I)I)I)
7D : (((((II)I)(II))I)I) ((((II)(II))I)(II)) ((((II)I)I)((II)I)) (((((II)I)I)I)(II))
8D : (((((II)I)(II))I)(II)) ((((II)(II))I)((II)I)) (((((II)I)I)I)((II)I))
6. Pentatorus ((((((II)I)I)I)I)I)
6D blobs:
Minor pair of tetratoruses ((((((II)I)I)I)I)) -> pentatorus
Quaternary pair of tetratoruses ((((((II)I)I)I))I) -> pentatorus
Tertiary pair of tetratoruses ((((((II)I)I))I)I) -> pentatorus
Secondary pair of tetratoruses ((((((II)I))I)I)I) -> pentatorus
Major pair of tetratoruses ((((((II))I)I)I)I) -> pentatorus
Two tetratoruses (((((((I)I)I)I)I)I) -> pentatorus
5D slabs:
Minor quartet of tritoruses (((((((II)I)I)I))) -> minor pair of tetratoruses, quaternary pair of tetratoruses
Tertiary/minor quartet of tritoruses ((((((II)I)I))I)) -> minor pair of tetratoruses, tertiary pair of tetratoruses
Secondary/minor quartet of tritoruses ((((((II)I))I)I)) -> minor pair of tetratoruses, secondary pair of tetratoruses
Major/minor quartet of tritoruses ((((((II))I)I)I)) -> minor pair of tetratoruses, major pair of tetratoruses
Two minor pairs of tritoruses ((((((I)I)I)I)I)) -> minor pair of tetratoruses, two tetratoruses
Tertiary quartet of tritoruses ((((((II)I)I)))I) -> quaternary pair of tetratoruses, tertiary pair of tetratoruses
Secondary/tertiary quartet of tritoruses ((((((II)I))I))I) -> quaternary pair of tetratoruses, secondary pair of tetratoruses
Major/tertiary quartet of tritoruses ((((((II))I)I))I) -> quaternary pair of tetratoruses, major pair of tetratoruses
Two tertiary pairs of tritoruses ((((((I)I)I)I))I) -> quaternary pair of tetratoruses, two tetratoruses
Secondary quartet of tritoruses ((((((II)I)))I)I) -> tertiary pair of tetratoruses, secondary pair of tetratoruses
Major/secondary quartet of tritoruses ((((((II))I))I)I) -> tertiary pair of tetratoruses, major pair of tetratoruses
Two secondary pairs of tritoruses ((((((I)I)I))I)I) -> tertiary pair of tetratoruses, two tetratoruses
Major quartet of tritoruses ((((((II)))I)I)I) -> secondary pair of tetratoruses, major pair of tetratoruses
Two major pairs of tritoruses ((((((I)I))I)I)I) -> secondary pair of tetratoruses, two tetratoruses
Four tritoruses ((((((I))I)I)I)I) -> major pair of tetratoruses, two tetratoruses
Empty slab (((((()I)I)I)I)I) -> two tetratoruses (x2)
4D slices:
Minor octet of ditoruses ((((((II)I)I)))) -> minor quartet of tritoruses, tertiary/minor quartet of tritoruses, tertiary quartet of tritoruses
Medium/minor/minor octet of ditoruses ((((((II)I))I))) -> minor quartet of tritoruses, secondary/minor quartet of tritoruses, secondary/tertiary quartet of tritoruses
Major/minor/minor octet of ditoruses ((((((II))I)I))) -> minor quartet of tritoruses, major/minor quartet of tritoruses, major/tertiary quartet of tritoruses
Two minor quartets of ditoruses ((((((I)I)I)I))) -> minor quartet of tritoruses, two minor pairs of tritoruses, two tertiary pairs of tritoruses
Medium/medium/minor octet of ditoruses ((((((II)I)))I)) -> tertiary/minor quartet of tritoruses, secondary/minor quartet of tritoruses, secondary quartet of tritoruses
Major/medium/minor octet of ditoruses (((((II))I))I)) -> tertiary/minor quartet of tritoruses, major/minor quartet of tritoruses, major/secondary quartet of tritoruses
Two medium/minor quartets of ditoruses (((((I)I)I))I)) -> tertiary/minor quartet of tritoruses, two minor pairs of tritoruses, two secondary pairs of tritoruses
Major/major/minor octet of ditoruses ((((((II)))I)I)) -> secondary/minor quartet of tritoruses, major/minor quartet of tritoruses, major quartet of tritoruses
Two major/minor quartets of ditoruses ((((((I)I))I)I)) -> secondary/minor quartet of tritoruses, two minor pairs of tritoruses, two major pairs of tritoruses
Four minor pairs of ditoruses ((((((I))I)I)I)) -> major/minor quartet of tritoruses, two minor pairs of tritoruses, four tritoruses
Empty slice A (((((()I)I)I)I)) -> two minor pairs of tritoruses (x2), empty slab
Medium octet of ditoruses ((((((II)I))))I) -> tertiary quartet of tritoruses, secondary/tertiary quartet of tritoruses, secondary quartet of tritoruses
Major/medium/medium octet of ditoruses ((((((II))I)))I) -> tertiary quartet of tritoruses, major/tertiary quartet of tritoruses, major/secondary quartet of tritoruses
Two medium quartets of ditoruses ((((((I)I)I)))I) -> tertiary quartet of tritoruses, two tertiary pairs of tritoruses, two secondary pairs of tritoruses
Major/major/medium octet of ditoruses ((((((II)))I))I) -> secondary/tertiary quartet of tritoruses, major/tertiary quartet of tritoruses, major quartet of tritoruses
Two major/medium quartets of ditoruses ((((((I)I))I))I) -> secondary/tertiary quartet of tritoruses, two tertiary pairs of tritoruses, two major pairs of tritoruses
Four medium pairs of ditoruses ((((((I))I)I))I) -> major/tertiary quartet of tritoruses, two tertiary pairs of tritoruses, four tritoruses
Empty slice B (((((()I)I)I))I) -> two tertiary pairs of tritoruses (x2), empty slab
Major octet of ditoruses ((((((II))))I)I) -> secondary quartet of tritoruses, major/secondary quartet of tritoruses, major quartet of tritoruses
Two major quartets of ditoruses ((((((I)I)))I)I) -> secondary quartet of tritoruses, two secondary pairs of tritoruses, two major pairs of tritoruses
Four major pairs of ditoruses ((((((I))I))I)I) -> major/secondary quartet of tritoruses, two secondary pairs of tritoruses, four tritoruses
Empty slice C (((((()I)I))I)I) -> two secondary pairs of tritoruses (x2), empty slab
Eight ditoruses ((((((I)))I)I)I) -> major quartet of tritoruses, two major pairs of tritoruses, four tritoruses
Empty slice D (((((()I))I)I)I) -> two major pairs of tritoruses (x2), empty slab
Empty slice E (((((())I)I)I)I) -> four tritoruses (x2), empty slab
3D cuts:
Minor 16-plet of toruses ((((((II)I))))) -> minor octet of ditoruses, medium/minor/minor octet of ditoruses, medium/medium/minor octet of ditoruses, medium octet of ditoruses
Major/minor/minor/minor 16-plet of toruses ((((((II))I)))) -> minor octet of ditoruses, major/minor/minor octet of ditoruses, major/medium/minor octet of ditoruses, major/medium/medium octet of ditoruses
Two minor octets of toruses ((((((I)I)I)))) -> minor octet of ditoruses, two minor quartets of ditoruses, two medium/minor quartets of ditoruses, two medium quartets of ditoruses
Major/major/minor/minor 16-plet of toruses ((((((II)))I))) -> medium/minor/minor octet of ditoruses, major/minor/minor octet of ditoruses, major/major/minor octet of ditoruses, major/major/medium octet of ditoruses
Two major/minor/minor octets of toruses ((((((I)I))I))) -> medium/minor/minor octet of ditoruses, two minor quartets of ditoruses, two major/minor quartets of ditoruses, two major/medium quartets of ditoruses
Four minor quartets of toruses ((((((I))I)I))) -> major/minor/minor octet of ditoruses, two minor quartets of ditoruses, four minor pairs of ditoruses, four medium pairs of ditoruses
Empty cut A (((((()I)I)I))) -> two minor quartets of ditoruses (x2), empty slice A, empty slice B
Major/major/major/minor 16-plet of toruses ((((((II))))I)) -> medium/medium/minor octet of ditoruses, major/medium/minor octet of ditoruses, major/major/minor octet of ditoruses, major octet of ditoruses
Two major/major/minor octets of toruses ((((((I)I)))I)) -> medium/medium/minor octet of ditoruses, two medium/minor quartets of ditoruses, two major/minor quartets of ditoruses, two major quartets of ditoruses
Four major/minor quartets of toruses ((((((I))I))I)) -> major/medium/minor octet of ditoruses, two medium/minor quartets of ditoruses, four minor pairs of ditoruses, four major pairs of ditoruses
Empty cut B (((((()I)I))I)) -> two medium/minor quartets of ditoruses (x2), empty slice A, empty slice C
Eight minor pairs of toruses ((((((I)))I)I)) -> major/major/minor octet of ditoruses, two major/minor quartets of ditoruses, four minor pairs of ditoruses, eight ditoruses
Empty cut C (((((()I))I)I)) -> two major/minor quartets of ditoruses (x2), empty slice A, empty slice D
Empty cut D (((((())I)I)I)) -> four minor pairs of ditoruses (x2), empty slice A, empty slice E
Major 16-plet of toruses ((((((II)))))I) -> medium octet of ditoruses, major/medium/medium octet of ditoruses, major/major/medium octet of ditoruses, major octet of ditoruses
Two major octets of toruses ((((((I)I))))I) -> medium octet of ditoruses, two medium quartets of ditoruses, two major/medium quartets of ditoruses, two major quartets of ditoruses
Four major quartets of toruses ((((((I))I)))I) -> major/medium/medium octet of ditoruses, two medium quartets of ditoruses, four medium pairs of ditoruses, four major pairs of ditoruses
Empty cut E (((((()I)I)))I) -> two medium quartets of ditoruses (x2), empty slice B, empty slice C
Eight major pairs of toruses ((((((I)))I))I) -> major/major/medium octet of ditoruses, two major/medium quartets of ditoruses, four medium pairs of ditoruses, eight ditoruses
Empty cut F (((((()I))I))I) -> two major/medium quartets of ditoruses (x2), empty slice B, empty slice D
Empty cut G (((((())I)I))I) -> four medium pairs of ditoruses (x2), empty slice B, empty slice E
16 toruses ((((((I))))I)I) -> major octet of ditoruses, two major quartets of ditoruses, four major pairs of ditoruses, eight ditoruses
Empty cut H (((((()I)))I)I) -> two major quartets of ditoruses (x2), empty slice C, empty slice D
Empty cut I (((((())I))I)I) -> four major pairs of ditoruses (x2), empty slice C, empty slice E
Empty cut J (((((()))I)I)I) -> eight ditoruses (x2), empty slice D, empty slice E
7. Tiger tritorus (((((II)(II))I)I)I)
6D blobs:
Minor pair of tiger ditoruses (((((II)(II))I)I)) -> tiger tritorus
Tertiary pair of tiger ditoruses (((((II)(II))I))I) -> tiger tritorus
Secondary pair of tiger ditoruses (((((II)(II)))I)I) -> tiger ditorus
Secondary stack of two tetratoruses (((((II)(I))I)I)I) & (((((I)(II))I)I)I) -> tiger tritorus
5D slabs:
Minor quartet of tiger toruses (((((II)(II))I))) -> minor pair of tiger ditoruses, tertiary pair of tiger ditoruses, secondary pair of tiger ditoruses
Medium/minor quartet of tiger toruses (((((II)(II)))I)) -> minor pair of tiger ditoruses
Secondary stack of two minor pairs of tritoruses (((((II)(I))I)I)) & (((((I)(II))I)I)) -> minor pair of tiger ditoruses, secondary stack of two tetratoruses
Medium quartet of tiger toruses (((((II)(II))))I) -> tertiary pair of tiger ditoruses, secondary pair of tiger ditoruses
Secondary stack of two tertiary pairs of tritoruses (((((II)(I))I))I) & (((((I)(II))I))I) -> tertiary pair of tiger ditoruses, secondary stack of two tetratoruses
Secondary stack of two secondary pairs of tritoruses (((((II)(I)))I)I) & (((((I)(II)))I)I) -> secondary pair of tiger ditoruses, secondary stack of two tetratoruses
Empty slab (((((II)())I)I)I) & ((((()(II))I)I)I) -> secondary stack of two tetratoruses (x2)
2x2 array of tritoruses (((((I)(I))I)I)I) -> secondary stack of two tetratoruses (x2, in two different ways)
4D slices:
Minor octet of tigers (((((II)(II))))) -> minor quartet of tiger toruses, medium/minor quartet of tiger toruses, medium quartet of tiger toruses
Medium stack of two minor quartets of ditoruses (((((II)(I))I))) & (((((I)(II))I))) -> minor quartet of tiger toruses, secondary stack of two minor pairs of tritoruses, secondary stack of two tertiary pairs of tritoruses
Medium stack of two medium/minor quartets of ditoruses (((((II)(I)))I)) & (((((I)(II)))I)) -> medium/minor quartet of tiger toruses, secondary stack of two minor pairs of tritoruses, secondary stack of two secondary pairs of tritoruses
Empty slice A (((((II)())I)I)) & ((((()(II))I)I)) -> secondary stack of two minor pairs of tritoruses (x2), empty slab
2x2 array of minor pairs of ditoruses (((((I)(I))I)I)) -> secondary stack of two minor pairs of tritoruses (x2, in two different ways), 2x2 array of tritoruses
Medium stack of two medium quartets of ditoruses (((((II)(I))))I) & (((((I)(II))))I) -> medium quartet of tiger toruses, secondary stack of two tertiary pairs of tritoruses, secondary stack of two secondary pairs of tritoruses
Empty slice B (((((II)())I))I) & ((((()(II))I))I) -> secondary stack of two tertiary pairs of tritoruses (x2), empty slab
2x2 array of medium pairs of ditoruses (((((I)(I))I))I) -> secondary stack of two tertiary pairs of tritoruses (x2, in two different ways), 2x2 array of tritoruses
Empty slice C (((((II)()))I)I) & ((((()(II)))I)I) -> secondary stack of two secondary pairs of tritoruses (x2), empty slab
2x2 array of major pairs of ditoruses (((((I)(I)))I)I) -> secondary stack of two secondary pairs of tritoruses (x2, in two different ways), 2x2 array of tritoruses
Empty slice D (((((I)())I)I)I) & ((((()(I))I)I)I) -> empty slab, 2x2 array of tritoruses (x2)
3D cuts:
Vertical stack of two minor octets of toruses (((((II)(I))))) & (((((I)(II))))) -> minor octet of tigers, medium stack of two minor quartets of ditoruses, medium stack of two medium/minor quartets of ditoruses, medium stack of two medium quartets of ditoruses
Empty cut A (((((II)())I))) & ((((()(II))I))) -> medium stack of two minor quartets of ditoruses (x2), empty slice A, empty slice B
2x2 array of minor quartets of toruses (((((I)(I))I))) -> medium stack of two minor quartets of ditoruses (x2, in two different ways), 2x2 array of minor pairs of ditoruses, 2x2 array of medium pairs of ditoruses
Empty cut B (((((II)()))I)) & ((((()(II)))I)) -> medium stack of two medium/minor quartets of ditoruses (x2), empty slice A, empty slice C
2x2 array of major/minor quartets of toruses (((((I)(I)))I)) -> medium stack of two medium/minor quartets of ditoruses (x2, in two different ways), 2x2 array of minor pairs of ditoruses, 2x2 array of major pairs of ditoruses
Empty cut C (((((I)())I)I)) & ((((()(I))I)I)) -> empty slice A, 2x2 array of minor pairs of ditoruses (x2), empty slice D
Empty cut D (((((II)())))I) & ((((()(II))))I) -> medium stack of two medium quartets of ditoruses (x2), empty slice B, empty slice C
2x2 array of major quartets of toruses (((((I)(I))))I) -> medium stack of two medium quartets of ditoruses (x2, in two different ways), 2x2 array of medium pairs of ditoruses, 2x2 array of major pairs of ditoruses
Empty cut E (((((I)())I))I) & ((((()(I))I))I) -> empty slice B, 2x2 array of medium pairs of ditoruses (x2), empty slice D
Empty cut F (((((I)()))I)I) & ((((()(I)))I)I) -> empty slice C, 2x2 array of major pairs of ditoruses (x2), empty slice D
Empty cut G ((((()())I)I)I) -> empty slice D (x4, in two different ways)
10. Torus tiger ditorus (((((II)I)(II))I)I)
6D blobs:
Minor pair of torus tiger toruses (((((II)I)(II))I)) -> torus tiger ditorus
Tertiary pair of torus tiger toruses (((((II)I)(II)))I) -> torus tiger ditorus
Tertiary stack of two tetratoruses (((((II)I)(I))I)I) -> torus tiger ditorus
Major pair of tiger ditoruses (((((II))(II))I)I) -> torus tiger ditorus
Two tiger ditoruses (((((I)I)(II))I)I) -> torus tiger ditorus
5D slabs:
Minor quartet of torus tigers (((((II)I)(II)))) -> minor pair of torus tiger toruses, tertiary pair of torus tiger toruses
Tertiary stack of two minor pairs of tritoruses (((((II)I)(I))I)) -> minor pair of torus tiger toruses, tertiary stack of two tetratoruses
Major/minor quartet of tiger toruses (((((II))(II))I)) -> minor pair of torus tiger toruses, major pair of tiger ditoruses
Two minor pairs of tiger toruses (((((I)I)(II))I)) -> minor pair of torus tiger toruses, two tiger ditoruses
Tertiary stack of two tertiary pairs of tritoruses (((((II)I)(I)))I) -> tertiary pair of torus tiger toruses, tertiary stack of two tetratoruses
Major/medium quartet of tiger toruses (((((II))(II)))I) -> tertiary pair of torus tiger toruses, major pair of tiger ditoruses
Two medium pairs of tiger toruses (((((I)I)(II)))I) -> tertiary pair of torus tiger toruses, two tiger ditoruses
Empty slab A (((((II)I)())I)I) -> tertiary stack of two tetratoruses (x2)
Secondary stack of two major pairs of tritoruses (((((II))(I))I)I) -> tertiary stack of two tetratoruses, major pair of tiger ditoruses
Two secondary stacks of two tritoruses (((((I)I)(I))I)I) -> tertiary stack of two tetratoruses, two tiger ditoruses
Secondary stack of four tritoruses (((((I))(II))I)I) -> major pair of tiger ditoruses, two tiger ditoruses
Empty slab B ((((()I)(II))I)I) -> two tiger ditoruses (x2)
4D slices:
Minor stack of two minor quartets of ditoruses (((((II)I)(I)))) -> minor quartet of torus tigers, tertiary stack of two minor pairs of tritoruses, tertiary stack of two tertiary pairs of tritoruses
Major/minor/minor octet of tigers (((((II))(II)))) -> minor quartet of torus tigers, major/minor quartet of tiger toruses, major/medium quartet of tiger toruses
Two minor quartets of tigers (((((I)I)(II)))) -> minor quartet of torus tigers, two minor pairs of tiger toruses, two medium pairs of tiger toruses
Empty slice A (((((II)I)())I)) -> tertiary stack of two minor pairs of tritoruses (x2), empty slab A
Medium stack of two major/minor quartets of ditoruses (((((II))(I))I)) -> tertiary stack of two minor pairs of tritoruses, major/minor quartet of tiger toruses, secondary stack of two major pairs of tritoruses
Two medium stacks of two minor pairs of ditoruses (((((I)I)(I))I)) -> tertiary stack of two minor pairs of tritoruses, two minor pairs of tiger toruses, two secondary stacks of two tritoruses
Medium stack of four minor pairs of ditoruses (((((I))(II))I)) -> major/minor quartet of tiger toruses, two minor pairs of tiger toruses, secondary stack of four tritoruses
Empty slice B ((((()I)(II))I)) -> two minor pairs of tiger toruses (x2), empty slab B
Empty slice C (((((II)I)()))I) -> tertiary stack of two tertiary pairs of tritoruses (x2), empty slab A
Medium stack of two major/medium quartets of ditoruses (((((II))(I)))I) -> tertiary stack of two tertiary pairs of tritoruses, major/medium quartet of tiger toruses, secondary stack of two major pairs of tritoruses
Two medium stacks of two medium pairs of ditoruses (((((I)I)(I)))I) -> tertiary stack of two tertiary pairs of tritoruses, two medium pairs of tiger toruses, two secondary stacks of two tritoruses
Medium stack of four medium pairs of ditoruses (((((I))(II)))I) -> major/medium quartet of tiger toruses, two medium pairs of tiger toruses, secondary stack of four tritoruses
Empty slice D ((((()I)(II)))I) -> two medium pairs of tiger toruses (x2), empty slab B
Empty slice E (((((II))())I)I) -> empty slab A, secondary stack of two major pairs of tritoruses (x2)
Empty slice F (((((I)I)())I)I) -> empty slab A, two secondary stacks of two tritoruses (x2)
4x2 array of ditoruses (((((I))(I))I)I) -> secondary stack of two major pairs of tritoruses, two secondary stacks of two tritoruses, secondary stack of four tritoruses
Empty slice G ((((()I)(I))I)I) -> two secondary stacks of two tritoruses (x2), empty slab B
Empty slice H ((((())(II))I)I) -> secondary stack of four tritoruses (x2), empty slab B
3D cuts:
Empty cut A (((((II)I)()))) -> minor stack of two minor quartets of ditoruses (x2), empty slice A, empty slice C
Vertical stack of two major/minor/minor octets of toruses (((((II))(I)))) -> minor stack of two minor quartets of ditoruses, major/minor/minor octet of tigers, medium stack of two major/minor quartets of ditoruses, medium stack of two major/medium quartets of ditoruses
Two vertical stacks of two minor quartets of toruses (((((I)I)(I)))) -> minor stack of two minor quartets of ditoruses, two minor quartets of tigers, two medium stacks of two minor pairs of ditoruses, two medium stacks of two medium pairs of ditoruses
Vertical stack of four minor quartets of toruses (((((I))(II)))) -> major/minor/minor octet of tigers, two minor quartets of tigers, medium stack of four minor pairs of ditoruses, medium stack of four medium pairs of ditoruses
Empty cut B ((((()I)(II)))) -> two minor quartets of tigers (x2), empty slice B, empty slice D
Empty cut C (((((II))())I)) -> empty slice A, medium stack of two major/minor quartets of ditoruses (x2), empty slice E
Empty cut D (((((I)I)())I)) -> empty slice A, two medium stacks of two minor pairs of ditoruses (x2), empty slice F
4x2 array of minor pairs of toruses (((((I))(I))I)) -> medium stack of two major/minor quartets of ditoruses, two medium stacks of two minor pairs of ditoruses, medium stack of four minor pairs of ditoruses, 4x2 array of ditoruses
Empty cut E ((((()I)(I))I)) -> two medium stacks of two minor pairs of ditoruses (x2), empty slice B, empty slice G
Empty cut F ((((())(II))I)) -> medium stack of four minor pairs of ditoruses (x2), empty slice B, empty slice H
Empty cut G (((((II))()))I) -> empty slice C, medium stack of two major/medium quartets of ditoruses (x2), empty slice E
Empty cut H (((((I)I)()))I) -> empty slice C, two medium stacks of two medium pairs of ditoruses (x2), empty slice F
4x2 array of major pairs of toruses (((((I))(I)))I) -> medium stack of two major/medium quartets of ditoruses, two medium stacks of two medium pairs of ditoruses, medium stack of four medium pairs of ditoruses, 4x2 array of ditoruses
Empty cut I ((((()I)(I)))I) -> two medium stacks of two medium pairs of ditoruses (x2), empty slice D
Empty cut J ((((())(II)))I) -> medium stack of four medium pairs of ditoruses (x2), empty slice D, empty slice H
Empty cut K (((((I))())I)I) -> empty slice E, empty slice F, 4x2 array of ditoruses (x2)
Empty cut L ((((()I)())I)I) -> empty slice F (x2), empty slice G (x2)
Empty cut M ((((())(I))I)I) -> 4x2 array of ditoruses (x2), empty slice G, empty slice H
17. Ditorus tiger torus (((((II)I)I)(II))I)
6D blobs:
Minor pair of ditorus tigers (((((II)I)I)(II))) -> ditorus tiger torus
Quaternary stack of two tetratoruses (((((II)I)I)(I))I) -> ditorus tiger torus
Secondary pair of two torus tiger toruses (((((II)I))(II))I) -> ditorus tiger torus
Major[torus] pair of torus tiger toruses (((((II))I)(II))I) -> ditorus tiger torus
Two[torus] torus tiger toruses (((((I)I)I)(II))I) -> ditorus tiger torus
5D slabs:
Minor stack of two minor pairs of tritoruses (((((II)I)I)(I))) -> minor pair of ditorus tigers, quaternary stack of two tetratoruses
Medium/minor quartet of torus tigers (((((II)I))(II))) -> minor pair of ditorus tigers, secondary pair of two torus tiger toruses
Major[torus]/minor quartet of torus tigers (((((II))I)(II))) -> minor pair of ditorus tigers, major[torus] pair of torus tiger toruses
Two[torus] minor pairs of torus tigers (((((I)I)I)(II))) -> minor pair of ditorus tigers, two[torus] torus tiger toruses
Empty slab A (((((II)I)I)())I) -> quaternary stack of two tetratoruses (x2)
Tertiary stack of two secondary pairs of tritoruses (((((II)I))(I))I) -> quaternary stack of two tetratoruses, secondary pair of two torus tiger toruses
Tertiary stack of two major pairs of tritoruses (((((II))I)(I))I) -> quaternary stack of two tetratoruses, major[torus] pair of torus tiger toruses
Two tertiary stacks of two tritoruses (((((I)I)I)(I))I) -> quaternary stack of two tetratoruses, two[torus] torus tiger toruses
Major quartet of tiger toruses (((((II)))(II))I) -> secondary pair of two torus tiger toruses, major[torus] pair of torus tiger toruses
Two major[A] pairs of tiger toruses (((((I)I))(II))I) -> secondary pair of two torus tiger toruses, two[torus] torus tiger toruses
Four[torus] tiger toruses (((((I))I)(II))I) -> major[torus] pair of torus tiger toruses, two[torus] torus tiger toruses
Empty slab B ((((()I)I)(II))I) -> two[torus] torus tiger toruses (x2)
4D slices:
Empty slice A (((((II)I)I)())) -> minor stack of two minor pairs of tritoruses (x2), empty slab A
Minor stack of two medium/minor quartets of ditoruses (((((II)I))(I))) -> minor stack of two minor pairs of tritoruses, medium/minor quartet of torus tigers, tertiary stack of two secondary pairs of tritoruses
Minor stack of two major/minor quartets of ditoruses (((((II))I)(I))) -> minor stack of two minor pairs of tritoruses, major[torus]/minor quartet of torus tigers, tertiary stack of two major pairs of tritoruses
Two minor stacks of two minor pairs of ditoruses (((((I)I)I)(I))) -> minor stack of two minor pairs of tritoruses, two[torus] minor pairs of torus tigers, two tertiary stacks of two tritoruses
Major/major/minor octet of tigers (((((II)))(II))) -> medium/minor quartet of torus tigers, major[torus]/minor quartet of torus tigers, major quartet of tiger toruses
Two major[A]/minor quartets of tigers (((((I)I))(II))) -> medium/minor quartet of torus tigers, two[torus] minor pairs of torus tigers, two major[A] pairs of tiger toruses
Four minor pairs of tigers (((((I))I)(II))) -> major[torus]/minor quartet of torus tigers, two[torus] minor pairs of torus tigers, four[torus] tiger toruses
Empty slice B ((((()I)I)(II))) -> two[torus] minor pairs of torus tigers (x2), empty slab B
Empty slice C (((((II)I))())I) -> empty slab A, tertiary stack of two secondary pairs of tritoruses (x2)
Empty slice D (((((II))I)())I) -> empty slab A, tertiary stack of two major pairs of tritoruses (x2)
Empty slice E (((((I)I)I)())I) -> empty slab A, two tertiary stacks of two tritoruses (x2)
Medium stack of two major quartets of ditoruses (((((II)))(I))I) -> tertiary stack of two secondary pairs of tritoruses, tertiary stack of two major pairs of tritoruses, major quartet of tiger toruses
Two medium stacks of two major pairs of ditoruses (((((I)I))(I))I) -> tertiary stack of two secondary pairs of tritoruses, two tertiary stacks of two tritoruses, two major[A] pairs of tiger toruses
Four medium stacks of two ditoruses (((((I))I)(I))I) -> tertiary stack of two major pairs of tritoruses, two tertiary stacks of two tritoruses, four[torus] tiger toruses
Empty slice F ((((()I)I)(I))I) -> two tertiary stacks of two tritoruses (x2), empty slab B
Medium stack of eight ditoruses (((((I)))(II))I) -> major quartet of tiger toruses, two major[A] pairs of tiger toruses, four[torus] tiger toruses
Empty slice G (((()I))(II))I) -> two major[A] pairs of tiger toruses (x2), empty slab B
Empty slice H (((())I)(II))I) -> four[torus] tiger toruses (x2), empty slab B
3D cuts:
Empty cut A (((((II)I))())) -> empty slice A, minor stack of two medium/minor quartets of ditoruses (x2), empty slice C
Empty cut B (((((II))I)())) -> empty slice A, minor stack of two major/minor quartets of ditoruses (x2), empty slice D
Empty cut C (((((I)I)I)())) -> empty slice A, two minor stacks of two minor pairs of ditoruses (x2), empty slice E
Vertical stack of two major/major/minor octets of toruses (((((II)))(I))) -> minor stack of two medium/minor quartets of ditoruses, minor stack of two major/minor quartets of ditoruses, major/major/minor octet of tigers, medium stack of two major quartets of ditoruses
Two vertical stacks of two major/minor quartets of toruses (((((I)I))(I))) -> minor stack of two medium/minor quartets of ditoruses, two minor stacks of two minor pairs of ditoruses, two major[A]/minor quartets of tigers, two medium stacks of two major pairs of ditoruses
Four vertical stacks of two minor pairs of toruses (((((I))I)(I))) -> minor stack of two major/minor quartets of ditoruses, two minor stacks of two minor pairs of ditoruses, four minor pairs of tigers, four medium stacks of two ditoruses
Empty cut D ((((()I)I)(I))) -> two minor stacks of two minor pairs of ditoruses (x2), empty slice B, empty slice F
Vertical stack of eight minor pairs of toruses (((((I)))(II))) -> major/major/minor octet of tigers, two major[A]/minor quartets of tigers, four minor pairs of tigers, medium stack of eight ditoruses
Empty cut E ((((()I))(II))) -> two major[A]/minor quartets of tigers (x2), empty slice B, empty slice G
Empty cut F ((((())I)(II))) -> four minor pairs of tigers (x2), empty slice B, empty slice H
Empty cut G (((((II)))())I) -> empty slice C, empty slice D, medium stack of two major quartets of ditoruses (x2)
Empty cut H (((((I)I))())I) -> empty slice C, empty slice E, two medium stacks of two major pairs of ditoruses (x2)
Empty cut I (((((I))I)())I) -> empty slice D, empty slice E, four medium stacks of two ditoruses (x2)
Empty cut J ((((()I)I)())I) -> empty slice E (x2), empty slice F (x2)
8x2 array of toruses (((((I)))(I))I) -> medium stack of two major quartets of ditoruses, two medium stacks of two major pairs of ditoruses, four medium stacks of two ditoruses, medium stack of eight ditoruses
Empty cut K ((((()I))(I))I) -> two medium stacks of two major pairs of ditoruses (x2), empty slice F, empty slice G
Empty cut L ((((())I)(I))I) -> four medium stacks of two ditoruses (x2), empty slice F, empty slice H
Empty cut M ((((()))(II))I) -> medium stack of eight ditoruses (x2), empty slice G, empty slice H
18. Double tiger torus ((((II)(II))(II))I)
6D blobs:
Minor pair of double tigers ((((II)(II))(II))) -> double tiger torus
Tertiary stack of two tiger ditoruses ((((II)(II))(I))I) -> double tiger torus
Secondary stack of two torus tiger toruses ((((II)(I))(II))I) & ((((I)(II))(II))I) -> double tiger torus
5D slabs:
Minor stack of two minor pairs of tiger toruses ((((II)(II))(I))) -> minor pair of double tigers, tertiary stack of two tiger ditoruses
Secondary stack of two minor pairs of torus tigers ((((II)(I))(II))) & ((((I)(II))(II))) -> minor pair of double tigers, secondary stack of two torus tiger toruses
Empty slab A ((((II)(II))())I) -> tertiary stack of two tiger ditoruses (x2)
2x2 secondary/tertiary stack of tritoruses ((((II)(I))(I))I) & ((((I)(II))(I))I) -> tertiary stack of two tiger ditoruses, secondary stack of two torus tiger toruses
Empty slab B ((((II)())(II))I) & (((()(II))(II))I) -> secondary stack of two torus tiger toruses (x2)
2x2 array of torus tigers ((((I)(I))(II))I) -> secondary stack of two torus tiger toruses (x2, in two different ways)
4D slices:
Empty slice A ((((II)(II))())) -> minor stack of two minor pairs of tiger toruses (x2), empty slab A
2x2 medium/minor stack of minor pairs of ditoruses ((((II)(I))(I))) & ((((I)(II))(I))) -> minor stack of two minor pairs of tiger toruses, secondary stack of two minor pairs of torus tigers, 2x2 secondary/tertiary stack of tritoruses
Empty slice B ((((II)())(II))) & (((()(II))(II))) -> secondary stack of two minor pairs of torus tigers (x2), empty slab B
2x2 array of minor pairs of tigers ((((I)(I))(II))) -> secondary stack of two minor pairs of torus tigers (x2, in two different ways), 2x2 array of torus tigers
Empty slice C ((((II)(I))())I) & ((((I)(II))())I) -> empty slab A, 2x2 secondary/tertiary stack of tritoruses (x2)
Empty slice D ((((II)())(I))I) & (((()(II))(I))I) -> 2x2 secondary/tertiary stack of tritoruses (x2), empty slab B
2x2 array of medium stacks of two ditoruses ((((I)(I))(I))I) -> 2x2 secondary/tertiary stack of tritoruses (x2, in two different ways), 2x2 array of torus tigers
Empty slice E ((((I)())(II))I) & (((()(I))(II))I) -> empty slab B, 2x2 array of torus tigers (x2)
3D cuts:
Empty cut A ((((II)(I))())) & ((((I)(II))())) -> empty slice A, 2x2 medium/minor stack of minor pairs of ditoruses (x2), empty slice C
Empty cut B ((((II)())(I))) & ((()(II))(I))) -> 2x2 medium/minor stack of minor pairs of ditoruses (x2), empty slice B, empty slice D
2x2 array of vertical stacks of two minor pairs of toruses ((((I)(I))(I))) -> 2x2 medium/minor stack of minor pairs of ditoruses (x2, in two different ways), 2x2 array of minor pairs of tigers, 2x2 array of medium stacks of two ditoruses
Empty cut C ((((I)())(II))) & (((()(I))(II))) -> empty slice B, 2x2 array of minor pairs of tigers (x2), empty slice E
Empty cut D ((((II)())())I) & (((()(II))())I) -> empty slice C (x2), empty slice D (x2)
Empty cut E ((((I)(I))())I) -> empty slice C (x2, in two different ways), 2x2 array of medium stacks of two ditoruses (x2)
Empty cut F ((((I)())(I))I) & (((()(I))(I))I) -> empty slice D, 2x2 array of medium stacks of two ditoruses (x2), empty slice E
Empty cut G (((()())(II))I) -> empty slice E (x4, in two different ways)
27. Duotorus tiger torus ((((II)I)((II)I))I)
6D blobs:
Minor pair of duotorus tigers ((((II)I)((II)I))) -> duotorus tiger torus
Major[circle] pair of torus tiger toruses ((((II)I)((II)))I) & ((((II))((II)I))I) -> duotorus tiger torus
Two[circle] torus tiger toruses ((((II)I)((I)I))I) & ((((I)I)((II)I))I) -> duotorus tiger torus
5D slabs:
Major[circle]/minor quartet of torus tigers ((((II)I)((II)))) & ((((II))((II)I))) -> minor pair of duotorus tigers, major[circle] pair of torus tiger toruses
Two[circle] minor pairs of torus tigers ((((II)I)((I)I))) & ((((I)I)((II)I))) -> minor pair of duotorus tigers, two[circle] torus tiger toruses
Tertiary stack of four tritoruses ((((II)I)((I)))I) & ((((I))((II)I))I) -> major[circle] pair of torus tiger toruses, two[circle] torus tiger toruses
Major[A]/major[B] quartet of tiger toruses ((((II))((II)))I) -> major[circle] pair of torus tiger toruses (x2, in two different ways)
Two major[B] pairs of tiger toruses ((((I)I)((II)))I) & ((((II))((I)I))I) -> major[circle] pair of torus tiger toruses, two[circle] torus tiger toruses
Empty slab ((((II)I)(()I))I) & (((()I)((II)I))I) -> two[circle] torus tiger toruses (x2)
2x2 [A/B] array of torus tigers ((((I)I)((I)I))I) -> two[circle] torus tiger toruses (x2, in two different ways)
4D slices:
Minor stack of four minor pairs of ditoruses ((((II)I)((I)))) & ((((I))((II)I))) -> major[circle]/minor quartet of torus tigers, two[circle] minor pairs of torus tigers, tertiary stack of four tritoruses
Major[A]/major[B]/minor octet of tigers ((((II))((II)))) -> major[circle]/minor quartet of torus tigers (x2, in two different ways), major[A]/major[B] quartet of tiger toruses
Two major[B]/minor quartets of tigers ((((I)I)((II)))) & ((((II))((I)I))) -> major[circle]/minor quartet of torus tigers, two[circle] minor pairs of torus tigers, two major[B] pairs of tiger toruses
Empty slice A ((((II)I)(()I))) & (((()I)((II)I))) -> two[circle] minor pairs of torus tigers (x2), empty slab
2x2 [A/B] array of minor pairs of tigers ((((I)I)((I)I)) -> two[circle] minor pairs of torus tigers (x2, in two different ways), 2x2 [A/B] array of torus tigers
Empty slice B ((((II)I)(()))I) & (((())((II)I))I) -> tertiary stack of four tritoruses (x2), empty slab
Medium stack of four major pairs of ditoruses ((((II))((I)))I) & ((((I))((II)))I) -> tertiary stack of four tritoruses, major[A]/major[B] quartet of tiger toruses, two major[B] pairs of tiger toruses
Two medium stacks of four ditoruses ((((I)I)((I)))I) & ((((I))((I)I))I) -> tertiary stack of four tritoruses, two major[B] pairs of tiger toruses, 2x2 [A/B] array of torus tigers
Empty slice C (((()I)((II)))I) & ((((II))(()I))I) -> two major[B] pairs of tiger toruses (x2), empty slab
Empty slice D ((((I)I)(()I))I) & (((()I)((I)I))I) -> empty slab, 2x2 [A/B] array of torus tigers (x2)
3D cuts:
Empty cut A ((((II)I)(()))) & (((())((II)I))) -> minor stack of four minor pairs of ditoruses (x2), empty slice A, empty slice B
Vertical stack of four major/minor quartets of toruses ((((II))((I)))) & ((((I))((II)))) -> minor stack of four minor pairs of ditoruses, major[A]/major[B]/minor octet of tigers, two major[B]/minor quartets of tigers, medium stack of four major pairs of ditoruses
Two vertical stacks of four minor pairs of toruses ((((I)I)((I)))) & ((((I))((I)I))) -> minor stack of four minor pairs of ditoruses, two major[B]/minor quartets of tigers, 2x2 [A/B] array of minor pairs of tigers, two medium stacks of four ditoruses
Empty cut B (((()I)((II)))) & ((((II))(()I))) -> two major[B]/minor quartets of tigers (x2), empty slice A, empty slice C
Empty cut C ((((I)I)(()I))) & (((()I)((I)I))) -> empty slice A, 2x2 [A/B] array of minor pairs of tigers (x2), empty slice D
Empty cut D ((((II))(()))I) & (((())((II)))I) -> empty slice B, medium stack of four major pairs of ditoruses (x2), empty slice C
Empty cut E ((((I)I)(()))I) & (((())((I)I))I) -> empty slice B, two medium stacks of four ditoruses (x2), empty slice D
4x4 array of toruses ((((I))((I)))I) -> medium stack of four major pairs of ditoruses (x2, in two different ways), two medium stacks of four ditoruses (x2, in two different ways)
Empty cut F (((()I)((I)))I) & ((((I))(()I))I) -> two medium stacks of four ditoruses (x2), empty slice C, empty slice D
Empty cut G (((()I)(()I))I) -> empty slice D (x4, in two different ways)
32. Triger torus (((II)(II)(II))I)
6D blobs:
Minor pair of trigers (((II)(II)(II))) -> triger torus
Medium stack of 221-tiger 1-toruses (((II)(II)(I))I) & (((II)(I)(II))I) & (((I)(II)(II))I) -> triger torus
5D slabs:
Minor stack of two minor pairs of 221-tigers (((II)(II)(I))) & (((II)(I)(II))) & (((I)(II)(II))) -> minor pair of trigers, medium stack of 221-tiger 1-toruses
Empty slab (((II)(II)())I) & (((II)()(II))I) & ((()(II)(II))I) -> medium stack of 221-tiger 1-toruses (x2)
2x2 medium stack of 221-ditoruses (((II)(I)(I))I) & (((I)(II)(I))I) & (((I)(I)(II))I) -> medium stack of 221-tiger 1-toruses (x2, in two different ways)
4D slices:
Empty slice A ((((II)(II)())) & (((II)()(II))) & ((()(II)(II))) -> minor stack of two minor pairs of 221-tigers (x2), empty slab
2x2 vertical stack of minor pairs of spheritoruses (((II)(I)(I))) & (((I)(II)(I))) & (((I)(I)(II))) -> minor stack of two minor pairs of 221-tigers (x2, in two different ways), 2x2 medium stack of 221-ditoruses
Empty slice B (((II)(I)())I) & (((I)(II)())I) & (((II)()(I))I) & (((I)()(II))I) & ((()(II)(I))I) & ((()(I)(II))I) -> empty slab, 2x2 medium stack of 221-ditoruses (x2)
2x2x2 array of torispheres (((I)(I)(I))I) -> 2x2 medium stack of 221-ditoruses (x3, in three different ways)
3D cuts:
Empty cut A ((((II)(I)())) & ((((I)(II)())) & (((II)()(I))) & (((I)()(II))) & ((()(II)(I))) & ((()(I)(II))) -> empty slice A, 2x2 vertical stack of minor pairs of spheritoruses (x2), empty slice B
2x2x2 array of pairs of spheres (((I)(I)(I))) -> 2x2 vertical stack of minor pairs of spheritoruses (x3, in three different ways), 2x2x2 array of torispheres
Empty cut B ((((II)()())I) & (((()(II)())I) & (((()()(II))I) -> empty slice B (x4, in two different ways)
Empty cut C ((((I)(I)())I) & ((((I)()(I))I) & (((()(I)(I))I) -> empty slice B (x2, in two different ways), 2x2x2 array of torispheres (x2)
39. Tiger torus tiger ((((II)(II))I)(II))
6D blobs:
Minor stack of two tiger ditoruses ((((II)(II))I)(I)) -> tiger torus tiger
Medium pair of double tigers ((((II)(II)))(II)) -> tiger torus tiger
Secondary stack of two ditorus tigers ((((II)(I))I)(II)) & ((((I)(II))I)(II)) -> tiger torus tiger
5D slabs:
Empty slab A ((((II)(II))I)()) -> minor stack of two tiger ditoruses (x2)
Minor stack of two medium pairs of tiger ditoruses ((((II)(II)))(I)) -> minor stack of two tiger ditoruses, medium pair of double tigers
2x2 secondary/minor stack of tritoruses ((((II)(I))I)(I)) & ((((I)(II))I)(I)) -> minor stack of two tiger ditoruses, secondary stack of two ditorus tigers
Medium stack of two medium pairs of torus tigers ((((II)(I)))(II)) & ((((I)(II)))(II)) -> medium pair of double tigers, secondary stack of two ditorus tigers
Empty slab B ((((II)())I)(II)) & (((()(II))I)(II)) -> secondary stack of two ditorus tigers (x2)
2x2 [torus] array of torus tigers ((((I)(I))I)(II)) -> secondary stack of two ditorus tigers (x2, in two different ways)
4D slices:
Empty slice A ((((II)(II)))()) -> empty slab A, minor stack of two medium pairs of tiger ditoruses (x2)
Empty slice B ((((II)(I))I)()) & ((((I)(II))I)()) -> empty slab A, 2x2 secondary/minor stack of tritoruses (x2)
2x2 medium/minor stack of medium pairs of ditoruses ((((II)(I)))(I)) & ((((I)(II)))(I)) -> minor stack of two medium pairs of tiger ditoruses, 2x2 secondary/minor stack of tritoruses, medium stack of two medium pairs of torus tigers
Empty slice C ((((II)())I)(I)) & (((()(II))I)(I)) -> 2x2 secondary/minor stack of tritoruses (x2), empty slab B
2x2 array of minor stacks of two ditoruses ((((I)(I))I)(I)) -> 2x2 secondary/minor stack of tritoruses (x2, in two different ways), 2x2 [torus] array of torus tigers
Empty slice D ((((II)()))(II)) & (((()(II)))(II)) -> medium stack of two medium pairs of torus tigers (x2), empty slab B
2x2 [A/A] array of major[A] pairs of tigers ((((I)(I)))(II)) -> medium stack of two medium pairs of torus tigers (x2, in two different ways), 2x2 [torus] array of torus tigers
Empty slice E ((((I)())I)(II)) & (((()(I))I)(II)) -> empty slab B, 2x2 [torus] array of torus tigers (x2)
3D cuts:
Empty cut A ((((II)(I)))()) & ((((I)(II)))()) -> empty slice A, empty slice B, 2x2 medium/minor stack of medium pairs of ditoruses (x2)
Empty cut B ((((II)())I)()) & (((()(II))I)()) -> empty slice B (x2), empty slice C (x2)
Empty cut C ((((I)(I))I)()) -> empty slice B (x2, in two different ways), 2x2 array of minor stacks of two ditoruses (x2)
Empty cut D ((((II)()))(I)) & (((()(II)))(I)) -> 2x2 medium/minor stack of medium pairs of ditoruses (x2), empty slice C, empty slice D
2x2 array of two vertical stacks of two major pairs of toruses ((((I)(I)))(I)) -> 2x2 medium/minor stack of medium pairs of ditoruses (x2, in two different ways), 2x2 array of minor stacks of two ditoruses, 2x2 [A/A] array of major[A] pairs of tigers
Empty cut E ((((I)())I)(I)) & (((()(I))I)(I)) -> empty slice C, 2x2 array of minor stacks of two ditoruses (x2), empty slice E
Empty cut F ((((I)()))(II)) & (((()(I)))(II)) -> empty slice D, 2x2 [A/A] array of major[A] pairs of tigers (x2), empty slice E
Empty cut G (((()())I)(II)) -> empty slice E (x4, in two different ways)
42. Torus double tiger ((((II)I)(II))(II))
6D blobs:
Minor stack of two torus tiger toruses ((((II)I)(II))(I)) -> torus double tiger
Tertiary stack of two ditorus tigers ((((II)I)(I))(II)) -> torus double tiger
Major pair of double tigers ((((II))(II))(II)) -> torus double tiger
Two[tiger] double tigers ((((I)I)(II))(II)) -> torus double tiger
5D slabs:
Empty slab A ((((II)I)(II))()) -> minor stack of two torus tiger toruses (x2)
2x2 tertiary/minor stack of tritoruses ((((II)I)(I))(I)) -> minor stack of two torus tiger toruses, tertiary stack of two ditorus tigers
Minor stack of two major pairs of tiger toruses ((((II))(II))(I)) -> minor stack of two torus tiger toruses, major pair of double tigers
Two minor stacks of two tiger toruses ((((I)I)(II))(I)) -> minor stack of two torus tiger toruses, two[tiger] double tigers
Empty slab B ((((II)I)())(II)) -> tertiary stack of two ditorus tigers (x2)
Medium stack of two major[torus] pairs of torus tigers ((((II))(I))(II)) -> tertiary stack of two ditorus tigers, major pair of double tigers
Two[torus] medium stacks of two torus tigers ((((I)I)(I))(II)) -> tertiary stack of two ditorus tigers, two[tiger] double tigers
Medium stack of four torus tigers ((((I))(II))(II)) -> major pair of double tigers, two[tiger] double tigers
Empty slab C (((()I)(II))(II)) -> two[tiger] double tigers (x2)
4D slices:
Empty slice A ((((II)I)(I))()) -> empty slab A, 2x2 tertiary/minor stack of tritoruses (x2)
Empty slice B ((((II))(II))()) -> empty slab A, minor stack of two major pairs of tiger toruses (x2)
Empty slice C ((((I)I)(II))()) -> empty slab A, two minor stacks of two tiger toruses (x2)
Empty slice D ((((II)I)())(I)) -> 2x2 tertiary/minor stack of tritoruses (x2), empty slab B
2x2 medium/minor stack of major pairs of ditoruses ((((II))(I))(I)) -> 2x2 tertiary/minor stack of tritoruses, minor stack of two major pairs of tiger toruses, medium stack of two major[torus] pairs of torus tigers
Two 2x2 medium/minor stacks of ditoruses ((((I)I)(I))(I)) -> 2x2 tertiary/minor stack of tritoruses, two minor stacks of two tiger toruses, two[torus] medium stacks of two torus tigers
4x2 medium/minor stack of ditoruses ((((I))(II))(I)) -> minor stack of two major pairs of tiger toruses, two minor stacks of two tiger toruses, medium stack of four torus tigers
Empty slice E (((()I)(II))(I)) -> two minor stacks of two tiger toruses (x2), empty slab C
Empty slice F ((((II))())(II)) -> empty slab B, medium stack of two major[torus] pairs of torus tigers (x2)
Empty slice G ((((I)I)())(II)) -> empty slab B, two[torus] medium stacks of two torus tigers (x2)
4x2 [A/A] array of tigers ((((I))(I))(II)) -> medium stack of two major[torus] pairs of torus tigers, two[torus] medium stacks of two torus tigers, medium stack of four torus tigers
Empty slice H (((()I)(I))(II)) -> two[torus] medium stacks of two torus tigers (x2), empty slab C
Empty slice I (((())(II))(II)) -> medium stack of four torus tigers (x2), empty slab C
3D cuts:
Empty cut A ((((II)I)())()) -> empty slice A (x2), empty slice D (x2)
Empty cut B ((((II))(I))()) -> empty slice A, empty slice B, 2x2 medium/minor stack of major pairs of ditoruses (x2)
Empty cut C ((((I)I)(I))()) -> empty slice A, empty slice C, two 2x2 medium/minor stacks of ditoruses (x2)
Empty cut D ((((I))(II))()) -> empty slice B, empty slice C, 4x2 medium/minor stack of ditoruses (x2)
Empty cut E (((()I)(II))()) -> empty slice C (x2), empty slice E (x2)
Empty cut F ((((II))())(I)) -> empty slice D, 2x2 medium/minor stack of major pairs of ditoruses (x2), empty slice F
Empty cut G ((((I)I)())(I)) -> empty slice D, two 2x2 medium/minor stacks of ditoruses (x2), empty slice G
4x2 array of vertical stacks of two toruses ((((I))(I))(I)) -> 2x2 medium/minor stack of major pairs of ditoruses, two 2x2 medium/minor stacks of ditoruses, 4x2 medium/minor stack of ditoruses, 4x2 [A/A] array of tigers
Empty cut H (((()I)(I))(I)) -> two 2x2 medium/minor stacks of ditoruses (x2), empty slice E, empty slice H
Empty cut I (((())(II))(I)) -> 4x2 medium/minor stack of ditoruses (x2), empty slice E, empty slice I
Empty cut J ((((I))())(II)) -> empty slice F, empty slice G, 4x2 [A/A] array of tigers (x2)
Empty cut K (((()I)())(II)) -> empty slice G (x2), empty slice H (x2)
Empty cut L (((())(I))(II)) -> 4x2 [A/A] array of tigers (x2), empty slice H, empty slice I
Polyhedron Dude wrote:ICN5D, I got one thing to say about all of these toroidal pics and animations - AWESOME!!!
Polyhedron Dude wrote:ICN5D, I got one thing to say about all of these toroidal pics and animations - AWESOME!!!
quickfur wrote:I totally agree!!! These are some truly mindblowing animations. You should make a website dedicated to them.
Actually, since you already have a wiki account for uploading these images/animations, you might as well just start making wiki pages for their corresponding toratopes, and link to the images/animations from there.
A thought just occurred to me while looking at these crazy animations... what if there was an alternate universe where electron orbitals followed toratopic rules instead of the usual Schroedinger equation? Then you'd have crazy chemistries going on with orbitals shaped like these toratopes, where a state change would trigger a shift in the shape of the orbital akin to the transformations shown in your animations. So you'd have molecules where atoms are linked by concentric toroidal rings, sequences of toruses, etc.. You could get the most bizarre-looking molecules and the craziest chemical reactions.
Marek14 wrote:I see, so the last picture is rotation ((((Xy))x)(YI)), correct? So my ideas about these were incorrect and now I see why -- the main direction was in x axis and changed to y. This way, there are no real invariants in the rotation, unlike rotation ((((I))x)(XI)) where the trace of ditorus tiger ((((I)))(I)), 8x2 array of circles, would stay invariant throughout the rotation. Just as well that current 7D exploration no longer even attempts to explore rotations
((((I)))(I)) - 8x2 array of circles
O O O O O O O O
O O O O O O O O
((((II)))(I)) - simple rotation around bisecting line, divides trace into two separate 4x2 groups
|
O O O O|O O O O
|
O O O O|O O O O
|
((((I)))(II)) - simple rotation around bisecting line, divides trace into two separate 8x1 groups
O O O O O O O O
----------------------
O O O O O O O O
((((I)I))(I)) - complex rotation around non-intersecting line, isolates trace into two separate 4x2 groups, then rotate in opposing directions around two bisecting lines, dividing each into 2x2 groups
| |
O O|O O O O|O O
| |
O O|O O O O|O O
| |
CW CCW
((((I))I)(I)) - complex rotation around non-intersecting line, isolates trace into four separate 2x2 groups, then rotate around four bisecting lines, dividing each into 1x2 group
| | | |
O|O O|O O|O O|O
| | | |
O|O O|O O|O O|O
| | | |
CW CCW CW CCW
1. Put your images and gifs on wiki page of the particular toratopes to have a permanent storage for them.
2. You could try to combine the "main" toratope you're exploring with second, thinner, that goes through the hole to accentuate it better. In case of ditorus tiger, there could be a torus tiger inserted, for example.
ICN5D wrote:Marek14 wrote:1. Put your images and gifs on wiki page of the particular toratopes to have a permanent storage for them.
2. You could try to combine the "main" toratope you're exploring with second, thinner, that goes through the hole to accentuate it better. In case of ditorus tiger, there could be a torus tiger inserted, for example.
1) yeah, that sounds like a better idea. Right now, they're in the unboxed supercluster
2) How would that work? What should I expect to see? I remember you mentioned rendering chained toratopes, is that the same? Show how they link together through higher directions?
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