(o(oo),o) = o3o3o3o3/2*a3*c
o'oo"o = o4o3o4/3o
o"oo"o = o4/3o3o4/3o
o8"o = o3o3o *b4/3o
o'(o'o"o) = o4o4o4/3o3*b
o'(o"o'o) = o4o4/3o4o3*b
o"(o"o'o) = o4/3o4/3o4o3*b
o(o"o~o') = o3o4/3oinfino4*b
o(o,o~o) = o3o3/2oinfino3*b
(oo'o"o) = o3o4o4/3o3*a
(("o~(o'o)~o")') = oinfino4/3oinfino4/3*a4*c *b4*d
(o"o~o') o~o = o4/3oinfino4*a oinfino
(o,o~o) o~o = o3/2oinfino3*a oinfino
o'o"o o~o = o4o4/3o oinfino
o"o"o o~o = o4/3o4/3o oinfino
oo^6/5o o~o = o3o6/5o oinfino
(o^6o^6o,) o~o = o6o6o3/2*a oinfino
(o~o^6/5o^6) o~o = oinfino6/5o6*a oinfino
(o^6o^6/5o) o~o = o6o6/5o3*a oinfino
(o"o~o') o = o4/3oinfino4*a o
(o,o~o) o = o3/2oinfino3*a o
o'o"o o = o4o4/3o o
o"o"o o = o4/3o4/3o o
oo^6/5o o = o3o6/5o o
(o^6o^6o,) o = o6o6o3/2*a o
(o"o~o') o = o4/3oinfino4*a o
(o~o^6/5o^6) o = oinfino6/5o6*a o
(o^6o^6/5o) o = o6o6/5o3*a o
o~o o o = oinfino o o
o~o o o~o = oinfino o oinfino
4. (o(oo),x) = o3o3o3x3/2*a3*c  Tetrahedral hemitriangular tiling honeycomb. Cells are tets and trats (triangular tilings). Verf is an oho. Symbol is (o(oo),x). This one has hemicubic honeycomb symmetry, but is only wythoffian if it has quarter cubic honeycomb symmetry, also known as cyclotetrahedral symmetry.
18. o$'o = o3x3x *b4o, (oxxx) = o3x3x3x3*a  Truncated tetrahedraloctahedral honeycomb  also known as tatoh. Symbol is o$'o, or (oxxx). Cells are tuts, toes, and coes. Verf is a rectangular pyramid, the rectangle is a co verf.
19. (o(xx),x) = x3o3x3x3/2*a3*c  Truncated tetrahedral hemitriangulartiling honeycomb. Symbol is (o(xx),x). Cells are tuts, hexats (as truncated trats), and ohoes. Verf is a crossed quadrilateral pyramid. This has hemicubic honeycomb symmetry.
21. o'ox"x = o4o3x4/3x  Quasitruncated cubic honeycomb. Symbol is o'ox"x. Cells are quiths and octs, verf is a flat square pyramid.
33. (o(xx),o) = x3o3x3o3/2*a3*c  Rectified tetrahedral hemitriangulartiling honeycomb. Symbol is (o(xx),o). Cells are octs, ohoes, and thats. Verf is a crossed quadrilateral prism.
56. o'(x'x"o) = o4x4x4/3o3*b  Retrosphenoverted cubicuboctahedral cuboctahedral tomosquare tiling honeycomb. Symbol is o'(x'x"o). Cells are soccoes, coes, and tosquats.
62. o'(x"x'o) = o4x4/3x4o3*b  Wavaccocotsoth = Sphenoverted cubicuboctahedral cuboctahedral tomosquare tiling honeycomb. Symbol is o'(x"x'o). Cells are goccoes, coes, and quitsquats.
63. o'xo"x = o4x3o4/3x, x6"x = x3o3x *b4/3x  Quasirhombated cubic honeycomb. Symbol is o'xo"x, or x6"x. Cells are quercoes, cubes, and coes.
72. o'(x'x"x) = o4x4x4/3x3*b  Small cuboctatruncated cuboctahedral tomoctahedral truncated square tiling honeycomb. Symbol is o'(x'x"x). Cells are cotcoes, toes, and tosquats.
73. o'(x"x'x) = o4x4/3x4x3*b  Great cuboctatruncated cuboctahedral tomoctahedral truncated square tiling honeycomb. Symbol is o'(x"x'x). Cells are cotcoes, toes, and quitsquats.
74. o$"x = o3x3x *b4/3x  Great quasirhombated tetrahedraloctahedral honeycomb. Symbol is o$"x. Cells are quitcoes, quiths, and tuts.
75. o'xx"x = o4x3x4/3x, x$"x = x3x3x *b4/3x  Great quasirhombated cubic honeycomb. Symbol is o'xx"x, can also be x$"x. Cells are quitcoes, cubes, and toes.
77. x'(x'x"x) = x4x4x4/3x3*b  Small rhombicuboctahedral cubicuboctahedral prismatic tomosquare tiling honeycomb. Symbol is x'(x'x"x). Cells are gircoes, cotcoes, stops, and tosquats. Verf is an irregular tetrahedron.
78. x"(x"x'x) = x4/3x4/3x4x3*b  Great rhombicuboctahedral cubicuboctahedral prismatic tomosquare tiling honeycomb. Symbol is x"(x"x'x). Cells are quitcoes, cotcoes, ops, and quitsquats. Verf is an irregular tetrahedron.
79. x"xx"x = x4/3x3x4/3x  Omniquasitruncated cubic honeycomb. Symbol is x"xx"x. Cells are quitcoes and stops. Verf is a skewed disphenoid.
81. x'(x'x"o) = x4x4x4/3o3*b  Small cubicuboctahedral tomocubic prismatic truncated square tiling honeycomb. Symbol is x'(x'x"o). Cells are soccoes, tics, cubes, and tosquats.
83. x"(x"x'o) = x4/3x4/3x4o3*b  Goccotocpitsith = Great cubicuboctahedral tomocubic prismatic truncated square tiling honeycomb. Symbol is x"(x"x'o). Cells are goccoes, quiths, cubes, and quitsquats.
84. x'ox"x = x4o3x4/3x  Prismatoquasirhombated cubic honeycomb. Symbol is x'ox"x. Cells are quercoes, quiths, cubes, and stops.
86. o(o"x~x') = o3o4/3xinfinx4*b  Circumfacetocubic hemialternate square tiling honeycomb. Symbol is o(o"x~x') where ~ represents infinity. Cells are cubes and shas. Verf is a triangular crossed prism. This has doubled runcic cubic symmetry.
91. o(o,x~x) = o3o3/2xinfinx3*b  Circumfacetotetrahedral hemialternate triangular tiling honeycomb. Symbol is o(o,x~x). Cells are tets and thas. Verf is a triangular crossed prism. This has doubled cyclotetrahedral symmetry.
94. (oo'x"x) = o3o4x4/3x3*a  Gotactictosquath = Great tetrahedral cubic tomocubic tomosquare tiling honeycomb. Symbol is (oo'x"x). Cells are tets, cubes, quiths, and quitsquats. Verf is a flat triangular antipodium.
97. o6"x = o3o3x *b4/3x  Quasirhombated tetrahedral octahedral honeycomb. Symbol is o6"x. Cells are tets, cubes, and quercoes. Verf is a triangular retropodium.
102. (oo"x'x) = (ox'x"o) = o3x4x4/3o3*a  Small tetrahedral cubic tomocubic tomosquare tiling honeycomb. Symbol is (oo"x'x). Cells are tets, cubes, tics, and tosquats. Verf is a triangular retroantipodium.
108. o'(o'x"x) = o4o4x4/3x3*b  Great cubicuboctahedral octahedral square tiling honeycomb. Symbol is o'(o'x"x). Cells are goccoes, octs, and squats. Verf is a flattish square podium.
124. o'(o"x'x) = o4/3o4/3x4x3*b  Small cubicuboctahedral octahedral square tiling honeycomb. Symbol is o'(o"x'x). Cells are soccoes, octs, and squats. Verf is a crossed square podium.
131. x'(o'x"x) = x4o4x4/3x3*b  Small rhombicuboctahedral cubicuboctahedral prismatic square tiling honeycomb. Symbol is x'(o'x"x). Cells are sircoes, goccoes, stops, and squats.
140. (("x~(o'x)~x")') = oinfinx4/3xinfinx4/3*a4*c *b4*d  Discubicuboctahedral alternate square disquare apeirogonal tiling honeycomb. Symbol is (("x~(o'x)~x")') Cells are soccoes, goccoes, shas, and disquas.
143. x'(o"x'x) = x4o4/3x4x3*b  Great rhombicuboctahedral cubicuboctahedral prismatic square tiling honeycomb. Symbol is x'(o"x'x). Cells are quercoes, soccoes, ops, and squats.
144. x(o"x~x') = x3o4/3xinfinx4*b  Dirhombicuboctahedral apeiroprismatic alternate square tiling honeycomb. Symbol is x(o"x~x'). Cells are sircoes, quercoes, azips, and shas.
168. o(o,o~x) = o3o3/2oinfinx3*b  Ditetrahedronary tetrahedral hemiditrigonal triangular tiling honeycomb. Symbol is o(o,o~x). Cells are tets and ditathas. Verf is an inflectoverted co, which looks like four tets attached at a point. Has cyclotetrahedral symmetry.
178. (o"x~x') o~x = o4/3xinfinx4*a oinfinx  Square hemiapeirogonal prismatic honeycomb. Symbol is (o"x~x') o~x. Cells are cubes and azips. This is from the chon regiment, because chon can be considered as the square tiling prismatic honeycomb. Verf is a crossed quadrilateral dipyramid, which has 180 degree dihedral angles between two right triangles.
182. (o,o~x) o~x = o3/2oinfinx3*a oinfinx  Ditrigonal triangular hemiapeirogonal prismatic honeycomb. Symbol is (o,o~x) o~x. Cells are trips and azips. Verf is a dipyramid of a ditrigon.
185. (o,x~x) o~x = o3/2xinfinx3*a oinfinx  Triangular hemiapeirogonal prismatic honeycomb. Symbol is (o,x~x) o~x. Cells are trips and azips. Verf is a crossed quadrilateral dipyramid.
190. o'x"x o~x = o4x4/3x oinfinx, x"x"x o~x = x4/3x4/3x oinfinx  Quasitruncated square prismatic honeycomb. Symbol is o'x"x o~x, also x"x"x o~x. Verf is an isosceles triangle dipyramid.
192. ox^6/5x o~x = o3x6/5x oinfinx  Quasitruncated hexagonal prismatic honeycomb. Symbol is ox^6/5x o~x. Cells are trips and 12/5ps (dodecagrammic prisms). Verf is an isosceles triangle dipyramid.
194. (o^6x^6x,) o~x = o6x6x3/2*a oinfinx  Small trihexahexagonal prismatic honeycomb. Symbol is (o^6x^6x,) o~x. Cells are trips, hips, and twips. Verf is a crossed trapezoid dipyramid.
196. (o~x"x') o~x = (x"x~o') o~x = x4/3xinfino4*a oinfinx  Small disquare apeirogonal prismatic honeycomb. Symbol is (o~x"x') o~x. Cells are cubes, stops, and azips. Verf is a trapezoid dipyramid, which has a 180 degree dihedral angle.
198. (o~x'x") o~x = (x"o~x') o~x = x4/3oinfinx4*a oinfinx  Great disquare apeirogonal prismatic honeycomb. Symbol is (o~x'x") o~x. Cells are cubes, ops, and azips. Verf is a crossed trapezoid dipyramid, which has a 180 degree dihedral angle.
201. (o~x^6/5x^6) o~x = oinfinx6/5x6*a oinfinx  Small dihexagonal apeirogonal prismatic honeycomb. Symbol is (o~x^6/5x^6) o~x. Cells are hips, 12/5ps, and azips. Verf is a trapezoid dipyramid, which has a 180 degree dihedral angle.
203. (o~x^6x^6/5) o~x = (x~o^6/5x^6) o~x = xinfino6/5x6*a oinfinx  Great dihexagonal apeirogonal prismatic honeycomb. Symbol is (o~x^6x^6/5) o~x. Cells are hips, twips, and azips. Verf is a crossed trapezoid dipyramid, which has a 180 degree dihedral angle.
206. (o^6x^6/5x) o~x = o6o6/5x3*a oinfinx  Great trihexahexagonal prismatic honeycomb. Symbol is (o^6x^6/5x) o~x. Cells are trips, hips, and 12/5ps. Verf is a trapezoid dipyramid.
207. xo^6/5x o~x = x3o6/5x oinfinx  Quasirhombitrihexagonal prismatic honeycomb. Symbol is xo^6/5x o~x. Cells are trips, cubes, and hips. Verf is a crossed trapezoid dipyramid.
210. (x~x"x') o~x = (x"x~x') o~x = x4/3xinfinx4*a oinfinx  Disquare apeirogonal prismatic honeycomb. Symbol is (x~x"x') o~x. Cells are ops, stops, and azips. Verf is a scalene triangle dipyramid, which has a 180 degree dihedral angle.
212. (x~x^6/5x^6) o~x = xinfinx6/5x6*a oinfinx  Dihexagonal apeirogonal prismatic honeycomb. Symbol is (x~x^6/5x^6) o~x. Cells are twips, 12/5ps, and azips. Verf is a scalene triangle dipyramid, which has a 180 degree dihedral angle.
214. x'x"x o~x = x4x4/3x oinfinx  Rhombidisquare prismatic honeycomb. Symbol is x'x"x o~x. Cells are cubes, ops, and stops. Verf is a scalene triangle dipyramid.
215. (x^6/5x^6x) o~x = x6x6/5x3*a oinfinx  Trihexatruncated trihexagonal prismatic honeycomb. Symbol is (x^6/5x^6x) o~x. Cells are hips, twips, and 12/5ps. Verf is a scalene triangular dipyramid.
216. xx^6/5x o~x = x3x6/5x oinfinx  Omniquasitruncated trihexagonal prismatic honeycomb. Symbol is xx^6/5x o~x. Cells are cubes, hips, and 12/5ps. Verf is a scalene triangle dipyramid.
218. o's"s o~x = o4s4/3s oinfinx, s"s"s o~x = s4/3s4/3s oinfinx  Retrosnub square prismatic honeycomb. Symbol is o's"s o~x, or s"s"s o~x. Cells are trips and cubes. Verf is an irregular pentagrammic dipyramid.
219. (s~s"s') o~x = (s"s~s') o~x = s4/3sinfins4*a oinfinx  Snub square apeirogonal prismatic honeycomb. Symbol is (s~s"s') o~x. Cells are trips, cubes, and azips. Verf is an irregular nonconvex hexagonal dipyramid.
225. (o"x~x') x = o4/3xinfinx4*a x  Square hemiapeirogonal tiling prism. Symbol is (o"x~x') x. Verf is a crossed quadrilateral pyramid.
228. (o,o~x) x = o3/2oinfinx3*a x  Ditrigonal triangular tiling prism. Symbol is (o,o~x) x. Verf is a pyramid of a ditrigon.
230. (o,x~x) x = o3/2xinfinx3*a x  Triangular hemiapeirogonal tiling prism. Symbol is (o,x~x) x. Verf is a crossed quadrilateral pyramid.
233. o'x"x x = o4x4/3x x, x"x"x x = x4/3x4/3x x  Quasitruncated square tiling prism. Symbol is o'x"x x, also x"x"x x. Verf is an isosceles triangle pyramid.
235. ox^6/5x x = o3x6/5x x  Quasitruncated hexagonal tiling prism. Symbol is ox^6/5x x. Verf is an isosceles triangle pyramid.
237. (o^6x^6x,) x = o6x6x3/2*a x  Small trihexahexagonal tiling prism. Symbol is (o^6x^6x,) x. Verf is a crossed trapezoid pyramid.
239. (o~x"x') x = (x"x~o') x = x4/3xinfino4*a x  Small disquare apeirogonal tiling prism. Symbol is (o~x"x') x. Verf is a trapezoid pyramid.
240. (o~x'x") x = (x"o~x') x = x4/3oinfinx4*a x  Great disquare apeirogonal tiling prism. Symbol is (o~x'x") x. Verf is a crossed trapezoid pyramid.
242. (o~x^6/5x^6) x = oinfinx6/5x6*a x  Small dihexagonal apeirogonal tiling prism. Symbol is (o~x^6/5x^6) x. Verf is a trapezoid pyramid.
243. (o~x^6x^6/5) x = (x~o^6/5x^6) x = xinfino6/5x6*a x  Great dihexagonal apeirogonal tiling prism. Symbol is (o~x^6x^6/5) x. Verf is a crossed trapezoid pyramid.
245. (o^6x^6/5x) x = o6x6/5x3*a x  Great trihexahexagonal tiling prism. Symbol is (o^6x^6/5x) x. Verf is a trapezoid pyramid.
246. xo^6/5x x = x3o6/5x x  Quasirhombitrihexagonal tiling prism. Symbol is xo^6/5x x. Verf is a crossed trapezoid pyramid.
249. (x~x"x') x = (x"x~x') x = x4/3xinfinx4*a x  Disquare apeirogonal tiling prism. Symbol is (x~x"x') x. Verf is a scalene triangle pyramid.
250. (x~x^6/5x^6) x = xinfinx6/5x6*a x  Dihexagonal apeirogonal tiling prism. Symbol is (x~x^6/5x^6) x. Verf is a scalene triangle pyramid.
251. x'x"x x = x4x4/3x x  Rhombidisquare tiling prism. Symbol is x'x"x x. Verf is a scalene triangle pyramid.
252. (x^6/5x^6x) x = x6x6/5x3*a x  Trihexatruncated trihexagonal tiling prism. Symbol is (x^6/5x^6x) x. Verf is a scalene triangle pyramid.
253. xx^6/5x x = x3x6/5x x  Omniquasitruncated trihexagonal tiling prism. Symbol is xx^6/5x x. Verf is a scalene triangle pyramid.
255. o's"s x = o4s4/3s x, s"s"s x = s4/3s4/3s x  Retrosnub square tiling prism. Symbol is o's"s x, or s"s"s x. Verf is an irregular pentagrammic pyramid.
256. (s~s"s') x = (s"s~s') x = s4/3sinfins4*a x  Snub square apeirogonal tiling prism. Symbol is (s~s"s') x. Verf is an irregular nonconvex hexagonal pyramid.
260. o~s s x = oinfins2s x  Apeirogonal antiduoprism. Symbol is o~s s x. Verf is a trapezoid pyramid. This is the prism of the apeirogonal antiprism.
264. o~s s o~x = oinfins2s oinfinx  Apeirogonal antiprism prismatic honeycomb. Symbol is o~s s o~x. Cells are trips and azips. Verf is a trapezoid dipyramid where two of the right triangles are coplanar, this and the next honeycomb are copycats of the previous one. (263. Square tiling hemiantiprism.)
Hedrondude wrote:I call (x'x"x~) satsa.
I played with some of these before by sketching their verfs and getting regiment counts, although I have yet to list them in a spreadsheet.
Here are some good names to start with:
o'ox"x = quitch
o'xx"x = gaqrich
x'xx"x = gaquapech
x'ox"x = quiprich
x'xo"x = paqrich
o'(o'x"x) = gacoca  for great cubaticubatiapeiratic honeycomb
o'(x"x'o) = wavicoca
x'(o'x"x) = skivpacoca
o(x"x~o') = wavicac  sphenoverted cubitiapeiraticubatic honeycomb
I'll coin more soon.
Jonathan B.
quitch  quasitruncated cubic honeycomb
gaqrich  great quasirhombated cubic honeycomb
gaquapech  great quasiprismated cubic honeycomb
quiprich  quasi prismatorhombated cubic honeycomb
paqrich  prismatoquasirhombated cubic honeycomb
wavicoca  sphenoverted cubaticubatiapeiratic honeycomb
skivpacoca  small skewverted prismatocubaticubatiapeiratic honeycomb
Klitzing wrote:Hehe Wendy, polychoronlover and I just were after the nonconvex apeirochora, not the apeirotera ...
But good to know  even so your lamiate namings surely are hard to decode ...
 rk
 Code: Select all
4. (o(oo),x) = o3o3o3x3/2*a3*c  Tetrahedral hemitriangular tiling honeycomb. Cells are tets and trats (triangular tilings). Verf is an oho. Symbol is (o(oo),x). This one has hemicubic honeycomb symmetry, but is only wythoffian if it has quarter cubic honeycomb symmetry, also known as cyclotetrahedral symmetry.
19. (o(xx),x) = x3o3x3x3/2*a3*c  Truncated tetrahedral hemitriangulartiling honeycomb. Symbol is (o(xx),x). Cells are tuts, hexats (as truncated trats), and ohoes. Verf is a crossed quadrilateral pyramid. This has hemicubic honeycomb symmetry.
33. (o(xx),o) = x3o3x3o3/2*a3*c  Rectified tetrahedral hemitriangulartiling honeycomb. Symbol is (o(xx),o). Cells are octs, ohoes, and thats. Verf is a crossed quadrilateral prism.
(B(CA),D) = A3B3C3D3/2*a3*c =
_A_
_3  3/2_
B_ 3 _D
3__3
C
1D
1 horogon, thus the square, cubic, and tesseractic tilings.
2D
Wythoffian
1 x4o4o o4x4o x4o4x
2 x3o6o s3s3s3z LA1 LB1
3 x6o3o x3x6o x3x3x3z
4 o3x6o x3x3o3z
5 x4x4o x4x4x #
6 x6x3o #
7 x3o6x #
8 x3x6x #
9 s3s6s
10 s4s4s #
Laminates
11 LPC1 #
3D
Wythoffian
1 x4o3o4o x4o3o4x
12 o4x3o4o
13 x3o4oAo x3o3x3o3z LA2
14 x3x3o3o3z
15 x3x4oAo x3x3x3o3z
16 x3o4xAo #
17 x4x3o4o #
18 x4o3x4o #
19 o4x3x4o x3x4o3x x3x3x3x3z
20 x3x4xAo #
21 x4x3x4o #
22 x4x3o4x #
23 x4x3x4x #
Laminates
24 LB2
25 LC2
26 LPA2 #
27 LPB2 #
28 LPC2 #
4D
29 55 products, formed from elements 211
Wythoffian
...
Wythoff  snub
s3s4o3o3o = s3s3s4o3o #
Laminates
LPA3 LC1A2 ##
LB3 LPB3 LC1B2 .##
LC3 LPB3 LC1C2 .#.
polychoronlover wrote:Thanks for pointing out my errors! Were there any other errors, or known honeycombs that I missed?
Also, are Paqrich and Quiprich distinct? The only nonconvex prismatorhombate regiment I could find contained something I called the prismatoquasirhombated cubic honeycomb as the second member. But that was x"ox"x, not x"ox'x or x'ox"x.
EDIT: When I wrote x'ox"x as the symbol for the honeycomb in my document, I meant x"ox"x.
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140. (("x~(o'x)~x")') = oinfinx4/3xinfinx4/3*a4*c *b4*d  Discubicuboctahedral alternate square disquare apeirogonal tiling honeycomb. Symbol is (("x~(o'x)~x")') Cells are soccoes, goccoes, shas, and disquas.
o where
/\
/ P*\ P = 3, 4, 6
/  \ P* = 3/2, 4/3, 6/5 (resp.)
U _o_ P U = infin (always)
/ _P U_ \
/_ _\
oP*o
o where

3 P = 3, 4, 6
 P* = 3/2, 4/3, 6/5 (resp.)
_o_ U = infin (always)
_P P*
_ _
oUo
Klitzing wrote:Btw., you speak of "rhombisnub uniform tilings" (plural). Which else do you refer to?
283. Octahemioctahedral tomoctahedral hemitrihexagonal tiling honeycomb. Cells are ohoes, toes, and thats.
284. Tomoctahedral intercepted disoctahedral cuboctahedral cubohemioctahedral hemitrihexagonal tiling honeycomb. Cells are octs (in two orientations), coes, choes, toes, and thats.
285. Tomoctahedral intercepted disoctahedral octahemioctahedral hemialternate hexagonal tiling hemialternate triangular tiling honeycomb. Cells are octs in two different orientations, ohoes, toes, hohas, and thas.
286. Cuboctahedral cubohemioctahedral tomoctahedral hemialternate hexagonal tiling hemialternate triangular tiling honeycomb. Cells are octs in two different orientations, coes, choes, toes, hohas, and thas.
287. Tomoctahedral intercepted disoctahedral cuboctahedral octahemioctahedral hemialternate square hemialternate hexagonal tiling honeycomb. Cells are octs in two different orientations, coes, ohoes, toes, shas, and hohas.
288. Tomoctahedral intercepted disoctahedral cuboctahedral hemitrihexagonal tiling hemialternate square tiling hemialternate hexagonal tiling honeycomb. Cells are octs in two different orientations, coes, toes, thats, shas, and hohas.
289. Tomoctahedral intercepted disoctahedral octahemioctahedral cubohemioctahedral hemialternate square hemialternate triangular tiling honeycomb. Cells are octs in two different orientations, ohoes, choes, toes, shas, and thas.
290. Tomoctahedral intercepted disoctahedral cubohemioctahedral hemialternate square tiling hemialternate triangular tiling hemitrihexagonal tiling honeycomb. Cells are octs in two different orientations, choes, toes, thats, thas, and shas.
291. Tomoctahedral intercepted cuboctahedral hemitrihexagonal tiling hemialternate square tiling honeycomb. Cells are coes, toes, thats, and shas.
292. Octahemioctahedral cubohemioctahedral tomoctahedral hemialternate square tiling hemialternate triangular tiling honeycomb. Cells are ohoes, choes, toes, shas, and thas.
293. Cubohemioctahedral tomoctahedral hemialternate square tiling hemialternate hexagonal tiling honeycomb. Cells are choes, toes, shas, and hohas.
294. Cubohemioctahedral octahemioctahedral hemialternate square tiling hemitrihexagonal tiling hemialternate hexagonal tiling honeycomb. Cells are choes, ohoes, shas, thats, and hohas.
295. Cuboctahedral apeiroprismatic hemialternate triangular tiling honeycomb. Cells are coes, azips, and thas.
username5243 wrote:I know it's bumping an old thread, but I have a question related to this: Has anyone investigated the starry 4D honeycombs yet? There are some interesting regiments there that I'm somewhat curious how to count. For reference, I will post the convex 4D honeycombs and what I know of their regiments...
polychoronlover wrote:username5243 wrote:I know it's bumping an old thread, but I have a question related to this: Has anyone investigated the starry 4D honeycombs yet? There are some interesting regiments there that I'm somewhat curious how to count. For reference, I will post the convex 4D honeycombs and what I know of their regiments...
I was looking into these a bit. One of the more interesting things I found was a family with diagram like so: o3o3o4o3o4/3 *a. It includes the lieutenant of the x3o3o4o3x regiment, as well as the head of its conjugate regiment, a "doublecovered" version of a o3o3o4x3o, and even some afdeclike members with vertex figures of the form a b3o  c o3d. These regiments seem to even include afdec members as potential facets, and may have over 1000 members!
Also, I found a "novel" tetracomb (one that does not have anything with a linear diagram in its regiment), o4o3o4x4/3x3 *c. It is interesting because the vertex figure is an octahedral podium whose "crossed" faceted form creates the conjugate, while a similar spherical polyteron, o3o3o4x4/3x3 *c, has a tetrahedral podium as its verf, whose crossed form is an antipodium instead.
oNo3o4x4/3x3 *c is also the only member of the oNo3o4o4/3o3 *c family which is not "skewed", does not contain cotcoes, and does not share its regiment with a polytope of the form ...x3o4/3x. It's interesting how it's so different in each case.
username5243 wrote:One other interesting one should be x3o4o3x3o, which has a square antifastegium verf. I'm pretty sure this one has a conjugate, but not sure about the symbol.
Indeed, that's curious, but a similar thing happens in lower dimensions. Take o3o3x4/3x4*a, which has a triangle podium, its crossed faceting is a trigonal crossed antipodium. o4o3x4/3x4*a has a square podium verf, and its crossed version is a square crossed podium. (In spherical 4D there is a regiment with a pentagon podium verf, and one of that one's crossed members has a pentagonal crossed antipodium verf.)
o
3
o
3 4
x 4/3 x
4 3
o
username5243 wrote:I think icot (tes verf) and hext (ico verf) may be related like that, since tes's edges are a subset of ico's.
username5243 wrote:BTW, I noticed after your latest revision of the list of honeycombs, you posted a list of new ones. Did you ever get around to adding those to your list of honeycombs?
username5243 wrote:In particular I'm curious about the one with a trigonal cupola verf  does it act like the stut phiddix regiment of 4D?
polychoronlover wrote:x4o3o3x4/3*a *b3d (trigonal cupolivert)
username5243 wrote:I was not talking about the antiprism. I was talking about this one from the new ones list...
chon regiment members w/ A(3) or C(3) verfs
octet regiment members w/ C(3) verfs
tich regiment
tatoh regiment
quitch regiment
rich regiment members w/ C(2)*A(1) or A(1)^3 verfs
srich regiment members w/ A(1)^2 verfs
wavicoca regiment members w/ A(1)^2 verfs
o3x4o~x4/3*b (wavicac) regiment
batch
grich, gratoh, cuteca, o3x4x~x4/3*b, gaqrich, gaqrahch, caquiteca
otch, cutpica, gactipeca, x3x4x~x4/3*b, x4x3x3x4/3*a *b3d, x4/3x4x3/2x3*a *a~c *b4d, gaquapech, quequapech, caquitpica, gacquitpica
prich regiment
quiprich regiment
gepdica regiment
gapdica regiment
x3x4o~x4/3*b regiment
x4x3o3x4/3*a *b3d regiment
chon regiment members w/ A(2) verfs
batatoh regiment
'gotactictosquath' regiment
ratoh regiment
rich regiment members w/ C(2) verfs
gacoco regiment members w/ C(2) verfs
srich regiment members w/ A(1) verfs
skivpacoca regiment
wavicoca regiment members w/ A(1) verfs
x4o3x3x4/3*a *b3d regiment
rich regiment members w/ A(1)^2 verfs
gacoco regiment members w/ A(1)^2 verfs
octet regiment members w/ A(3) verfs
x4o3o3x4/3*a *b3d regiment members
prismatics and their regiments
prisms
regiment members of prisms
other slabs and their regiments
gyrates and elongates
polychoronlover wrote:o3x4x~x4/3*b
polychoronlover wrote:x3x4x~x4/3*b
polychoronlover wrote:x4x3x3x4/3*a *b3d
polychoronlover wrote:x4/3x4x3/2x3*a *a~c *b4d
polychoronlover wrote:x3x4o~x4/3*b
polychoronlover wrote:x4x3o3x4/3*a *b3d
polychoronlover wrote:'gotactictosquath'
polychoronlover wrote:x4o3x3x4/3*a *b3d
polychoronlover wrote:x4o3o3x4/3*a *b3d
_o_
_3  4_
o< 3 >o
3_  4/3
o
Klitzing wrote:
 Code: Select all
_o_
_3  4_
o< 3 >o
3_  4/3
o
First of all: the linearisation symbol of the above symmetry group you gave as "o4o3o3o4/3*a *b3d" is wrong, as the letter "d" likewise isn't a real node, rather it is a virtaul one too, which rereffers to the dth so far already provided real node from the left. Accordingly it ought be prefixed by an asterisk as well. So you'd write rather "o4o3o3o4/3*a *b3*d".
But you could try a different linearisation here as well, cutting open at a threefold node (instead of a normal twofold one) and you'd get e.g. the simpler symbol "o3o3o4/3o4*a3*c" instead.
Next I looked through your according decoration cases.(Here the symbols ^, <, v, and > refer to the accordingly shaped subdiagram.  All other decorations would use some Grünbaumian figure either as cell or as verf.)
 x3x3x4/3x4*a3*c  dicroch = dicubatirhombated cubihexagonal HC, cells are: ^ girco, < hexat, v quitco, > cotco
 o3x3x4/3x4*a3*c  ???, cells are: ^ sirco, < that, v quitco, > gocco
 x3o3x4/3x4*a3*c  dichac = dicubatihexacubatic HC, cells are: ^ tic, < that, v quith, > cotco
 x3x3o4/3x4*a3*c  skivcadach = small skewverted cubatiapeiroducubatic HC, cells are: ^ girco, < that, v querco, > socco
 o3o3x4/3x4*a3*c  stut cadoca = small tritrigonary cubatidicuubatiapeiratic HC, cells are: ^ cube, < trat, v quith, > gocco
 x3o3o4/3x4*a3*c  ???, cells are: ^ tic, < trat, v cube, > socco
You overlooked the "???" cases? At least the according namings are missing.
 rk
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