Klitzing wrote:Just as an addition to the former:
here is a display of a different application of the alternated faceting method, which does not conform with Mercurial's Intention.
This time I'm alternating the triangles of the small rhombicuboctahedron, s4o3x,
(again using the same color-coding as explained above), which (as mere sectioning) results in a variant of the truncated tetrahedron.
--- rk
4D spherical:
s3s3s3s - snip (snub pentachoron). Cells: 10 ikes, 20 octs, 60 tets.
s3s3s4s - snet (snub tesseract). Cells: 8 snics, 16 ikes, 24 squaps, 32 octs, 192 tets.
s3s4s3s - snico (snub icositetrachoron). Cells: 48 snics, 192 octs, 576 tets.
s3s3s5s - snahi (snub hecatonicosachoron. Cells: 120 snids, 600 ikes, 720 paps, 1200 octs, 7200 tets.
s3s3s *b3s = s3s3s4o = s3s4o3o - sadi (snub disicositetrachoron). Cells: 24 ikes, 24+96 tets. This one can be made uniform.
s2s3s3s - snittap (snub tetrahedral antiprism). Cells: 2 ikes, 8 octs, 6+24 tets.
s2s3s4s - sniccap (snub cubic antiprism). Cells: 2 snics, 6 squaps, 8 tets, 12+48 tets.
s2s3s5s - sniddap (snub dodecahedral antiprism). cells: 2 snids, 12 paps, 20 octs, 30+120 tets.
sps2sqs (p,q>2): p,q-dap (p,q-duoantiprism). Cells: 2q p-aps, 2p q-aps, 2pq tets.
s2s2sps (p > 2): 2,p-dap (2,p-duoantiprism). cells: 4 n-aps, 2p+4p tets.
s2s2s2s - hex (hexadecachoron). Cells: 16 tets) This one is uniform.
Honeycombs:
s3s4s3s - snich (snub cubic honeycomb). Cells, snics, squaps, tets.
s3s3s *b4s = s4s3s4o - ???. Cells: snics, ikes, tets (both main and snub).
s3s3s3s3*a = s3s3s *b4o = o4s3s4o - ????. Cells: ikes, tets.
5D spherical:
s3s3s3s3s - snix (snub hexateron). Facetes: 12 snips, 30 snittaps, 20 triddaps (3-3 duoantirprisms), 360 pens.
s3s3s3s4s - snan (snub penteract). Facets: 10 snets, 32 snips, 40 sniccaps, 80 snittaps, 80 tisdaps (3-4 duoantiprisms), 1920 pens.
s3s3s *b3s3s = s3s3s3s4o - ?????. Cells: 10 sadis, 32 snips, 40 snittaps, 80 ditdaps (2-3 duoantiprisms), 960 pens.
Tetracombs:
s4s3s3s4s - snettit (snub tesseractic tetracomb). Cells: snets, sniccaps, squiddaps (4-4 duoantiprisms), pens.
s3s3s *b3s4s = s4s3s3s4o - ??????. Facets: snets, sadis, snittaps, disdaps (2-4 duoantiprisms), pens.
s3s3s *b3s *b3s = s3s3s *b3s4o = o4s3s3s4o = s3s3s4o3o = o3o3o4s3s - sadit (snub disicositetrachoric tetracomb). Cells: sadis, hexes, pens. This one is uniform.
s3s3s4s3s = snicot (snub icositetrachoric tetracomb). Cells: snicoes, snets, sniccaps, snittaps, triddaps, pens.
s3s3s3s3s3*a - ?????. Cells, snips, pens.
username5243 wrote:I'd be interested in hearing about your project, especially the duals of the "gyrochoron" type dice (see Hedrondude's dice pages)...
I've meanwhile made a list of (full) snubs (including honeycombs) in 4 and 5 dimensions. Note that facets are not assumed to be generally uniform. I've only included prismatic groups in the 4D spherical cases.
- Code: Select all
4D spherical:
s3s3s3s - snip (snub pentachoron). Cells: 10 ikes, 20 octs, 60 tets.
s3s3s4s - snet (snub tesseract). Cells: 8 snics, 16 ikes, 24 squaps, 32 octs, 192 tets.
s3s4s3s - snico (snub icositetrachoron). Cells: 48 snics, 192 octs, 576 tets.
s3s3s5s - snahi (snub hecatonicosachoron. Cells: 120 snids, 600 ikes, 720 paps, 1200 octs, 7200 tets.
s3s3s *b3s = s3s3s4o = s3s4o3o - sadi (snub disicositetrachoron). Cells: 24 ikes, 24+96 tets. This one can be made uniform.
s2s3s3s - snittap (snub tetrahedral antiprism). Cells: 2 ikes, 8 octs, 6+24 tets.
s2s3s4s - sniccap (snub cubic antiprism). Cells: 2 snics, 6 squaps, 8 tets, 12+48 tets.
s2s3s5s - sniddap (snub dodecahedral antiprism). cells: 2 snids, 12 paps, 20 octs, 30+120 tets.
sps2sqs (p,q>2): p,q-dap (p,q-duoantiprism). Cells: 2q p-aps, 2p q-aps, 2pq tets.
s2s2sps (p > 2): 2,p-dap (2,p-duoantiprism). cells: 4 n-aps, 2p+4p tets.
s2s2s2s - hex (hexadecachoron). Cells: 16 tets) This one is uniform.
Honeycombs:
s3s4s3s - snich (snub cubic honeycomb). Cells, snics, squaps, tets.
s3s3s *b4s = s4s3s4o - ???. Cells: snics, ikes, tets (both main and snub).
s3s3s3s3*a = s3s3s *b4o = o4s3s4o - ????. Cells: ikes, tets.
5D spherical:
s3s3s3s3s - snix (snub hexateron). Facetes: 12 snips, 30 snittaps, 20 triddaps (3-3 duoantirprisms), 360 pens.
s3s3s3s4s - snan (snub penteract). Facets: 10 snets, 32 snips, 40 sniccaps, 80 snittaps, 80 tisdaps (3-4 duoantiprisms), 1920 pens.
s3s3s *b3s3s = s3s3s3s4o - ?????. Cells: 10 sadis, 32 snips, 40 snittaps, 80 ditdaps (2-3 duoantiprisms), 960 pens.
Tetracombs:
s4s3s3s4s - snettit (snub tesseractic tetracomb). Cells: snets, sniccaps, squiddaps (4-4 duoantiprisms), pens.
s3s3s *b3s4s = s4s3s3s4o - ??????. Facets: snets, sadis, snittaps, disdaps (2-4 duoantiprisms), pens.
s3s3s *b3s *b3s = s3s3s *b3s4o = o4s3s3s4o = s3s3s4o3o = o3o3o4s3s - sadit (snub disicositetrachoric tetracomb). Cells: sadis, hexes, pens. This one is uniform.
s3s3s4s3s = snicot (snub icositetrachoric tetracomb). Cells: snicoes, snets, sniccaps, snittaps, triddaps, pens.
s3s3s3s3s3*a - ?????. Cells, snips, pens.
username5243 wrote:Snich's verf should be similar to snip's verf - it should have 2 isosceles pentagons, 2 trapezoids, and 4 triangles. The next ones verf will be some stretched version of a teddi (sadi verf), with 3 pentagons and 5 triangles. The last one's (s3s3s3s3*a)'s verf will have 4 pentagons and 4 triangles, but I'm not quite sure what it's like.
Snix and snan (as well as snettit and snicot) have verfs with 2 snip-verf-types, 2 snittap-verf-types, 1 duoantiprism-verf-type (which I think is a blend of two wedges at their bases) and 5 tets. s3s3s *b3s3s and s3s3s *b3s4s will have 2 snip-verf-types, 1 teddi, 1 snittap-verf-type, 1 2,n-dap type (similar to the general duoantiprism verf, but the top edge of one of the wedges has collapsed to a point), and 5 tets. Sadit's verf has 4 teddis, 5 tets, and 1 oct, and in the uniform version it has all regular faces (Klitzing has its incmat on his site). Finally, s3s3s3s3s3*a's verf should have 5 snip-verfs and 5 tets.
I have no clue how the verfs actually can be constructed, but that's just based on their facets.
username5243 wrote:What do you mean by "tetrahedral wedge"?
My guess would be some kind of variant of the tet prism for the sectioning facets oof the 5D cases.
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