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.
Users browsing this forum: Google [Bot] and 1 guest