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The cubic honeycomb or cubic cellulation is the only proper regular space-filling tessellation (or honeycomb) in Euclidean 3-space made up of cubic cells...

prism cells, with an isosceles-trapezoidal pyramid vertex figure. The runcicantellated order-5 dodecahedral honeycomb is equivalent to the runcitruncated...

Biruncinated 7-cube Runcitruncated 7-cube Biruncitruncated 7-cube Runcicantellated 7-cube Biruncicantellated 7-cube Runcicantitruncated 7-cube Biruncicantitruncated...

honeycomb, t0,3{4,3,4}: The runcitruncated order-5 cubic honeycomb or runcicantellated order-4 dodecahedral honeycomb, , has truncated cube, rhombicosidodecahedron...

6-orthoplex Runcitruncated 6-cube Biruncitruncated 6-cube Runcicantellated 6-orthoplex Runcicantellated 6-cube Biruncitruncated 6-orthoplex Runcitruncated 6-orthoplex...

Runcitruncated 8-simplex Biruncitruncated 8-simplex Triruncitruncated 8-simplex Runcicantellated 8-simplex Biruncicantellated 8-simplex Runcicantitruncated 8-simplex...

four-dimensional Euclidean geometry, the runcicantellated 24-cell honeycomb is a uniform space-filling honeycomb. Runcicantellated icositetrachoric tetracomb/honeycomb...

(1+{\sqrt {2}}),\ \pm (1+2{\sqrt {2}}),\ \pm (1+2{\sqrt {2}})\right)} Runcicantellated penteract Prismatorhombated penteract (Acronym: prin) (Jonathan Bowers)...

prism cells, with an isosceles-trapezoidal pyramid vertex figure. The runcicantellated icosahedral honeycomb is equivalent to the runcitruncated icosahedral...

prism facets, with an isosceles-trapezoidal pyramid vertex figure. The runcicantellated order-6 dodecahedral honeycomb is the same as the runcitruncated order-5...

analogue of the rhombicuboctahedron. The runcitruncated tesseract, runcicantellated 16-cell, or prismatorhombated hexadecachoron is bounded by 80 cells:...

7-orthoplex Runcitruncated 7-orthoplex Biruncitruncated 7-orthoplex Runcicantellated 7-orthoplex Biruncicantellated 7-orthoplex Runcicantitruncated 7-orthoplex...

6-orthoplex Runcitruncated 6-cube Biruncitruncated 6-cube Runcicantellated 6-orthoplex Runcicantellated 6-cube Biruncitruncated 6-orthoplex Runcitruncated 6-orthoplex...

of the cuboctahedral cells into 8 and 16 each. It is also called a runcicantellated demitesseract in a D4 symmetry, giving 3 colors of cells, 8 for each...

In five-dimensional geometry, a steric 5-cube, steric 5-demicube or sterihalf 5-cube, is a convex uniform 5-polytope. There are unique 4 steric forms of...

Prismatorhombated heptapeton (Acronym: pril) (Jonathan Bowers) The vertices of the runcicantellated 6-simplex can be most simply positioned in 7-space as permutations...

In four-dimensional Euclidean geometry, the runcicantellated tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean...

In four-dimensional geometry, a runcinated 5-cell is a convex uniform 4-polytope, being a runcination (a 3rd order truncation, up to face-planing) of the...

In four-dimensional Euclidean geometry, the 4-simplex honeycomb, 5-cell honeycomb or pentachoric-dispentachoric honeycomb is a space-filling tessellation...

tiling facets, with an isosceles-trapezoidal pyramid vertex figure. The runcicantellated square tiling honeycomb is the same as the runcitruncated order-4 octahedral...

cube cells, with an isosceles-trapezoidal pyramid vertex figure. The runcicantellated order-4 dodecahedral honeycomb is the same as the runcitruncated order-5...

(±1,±1,±1,±3,±3,±5) with an odd number of plus signs. Runcicantellated demihexeract Runcicantellated 6-demicube Prismatorhombated hemihexeract (Acronym:...

tiling cells, with an isosceles-trapezoidal pyramid vertex figure. The runcicantellated hexagonal tiling honeycomb or runcitruncated order-6 tetrahedral honeycomb...

tiling cells, with an isosceles-trapezoidal pyramid vertex figure. The runcicantellated order-4 hexagonal tiling honeycomb is the same as the runcitruncated...

Prismatorhombated octaexon (acronym: paro) (Jonathan Bowers) The vertices of the runcicantellated 7-simplex can be most simply positioned in 8-space as permutations...

two decagonal prisms, one triangular prism, and one cuboctahedron. Runcicantellated 600-cell (Norman W. Johnson) Prismatorhombated hexacosichoron (Acronym:...

and octagonal prism facets, with a square pyramid vertex figure. The runcicantellated order-4 square tiling honeycomb is equivalent to the runcitruncated...

±1,±1,0) Runcicantellated pentacross Prismatorhombated triacontaditeron (Acronym: pirt) (Jonathan Bowers) The vertices of the runcicantellated 5-orthoplex...

exists as one of 64 orthant facets of the runcitruncated 6-orthoplex. Runcicantellated hexateron Biruncitruncated 5-simplex/hexateron Prismatorhombated hexateron...

1:1:2, with a mirrored sphenoid vertex figure. It is related to the runcicantellated cubic honeycomb. John Horton Conway calls this honeycomb a f-tCO-trille...

tetrahedral honeycomb is equivalent to the runcicantellated hexagonal tiling honeycomb. The runcicantellated order-6 tetrahedral honeycomb is equivalent...

and square tiling facets, with a square pyramid vertex figure. The runcicantellated order-4 octahedral honeycomb is the same as the runcitruncated square...

5-cell 60 5!/2! 8 (0, 1, 1, 2, 3) (3, 2, 2, 1, 0) Runcitruncated 5-cell Runcicantellated 5-cell 60 5!/2! 9 (0, 1, 2, 3, 4) Omnitruncated 5-cell 120 5!...

prism cells, with an isosceles-trapezoidal pyramid vertex figure. The runcicantellated order-5 hexagonal tiling honeycomb is the same as the runcitruncated...

6-simplex tetradecapeton (fe) (0,0,0,1,2,2,2) 14 84 280 490 420 140 12 Runcicantellated 6-simplex prismatorhombated heptapeton (pril) (0,0,0,1,2,2,3) 70 455...

with an odd number of plus signs. It has half the vertices of the runcicantellated 5-cube, as compared here in the B5 Coxeter plane projections: These...

Prismatotruncated hecatonicosaoctaexon (Potaz) 31 t0,2,3{3,3,3,3,3,4} Runcicantellated 7-orthoplex Prismatorhombated hecatonicosaoctaexon (Parz) 32 t1,2,3{3...

3} Tritruncated 6-simplex Tetradecapeton (fe) 12 t0,2,3{3,3,3,3,3} Runcicantellated 6-simplex Prismatorhombated heptapeton (pril) 13 t1,2,3{3,3,3,3,3}...

Prismatotruncated diacosipentacontahexazetton 39 t0,2,3{3,3,3,3,3,3,4} Runcicantellated 8-orthoplex Prismatorhombated diacosipentacontahexazetton 40 t1,2,3{3...

3} - {6}×{3} { }×r{3,3} rr{3,3,3} 9 (0,0,1,2,2,3) or (0,1,1,2,3,3) Runcicantellated 5-simplex prismatorhombated hexateron (pirx) 47 255 570 540 180 t0...

Runcitruncated 7-simplex (patto) (0,0,0,0,1,1,2,3) 4620 840 19 t0,2,3 Runcicantellated 7-simplex (paro) (0,0,0,0,1,2,2,3) 3360 840 20 t1,2,3 Bicantitruncated...

signs. A runcicantic 7-cube, h2,3{4,35}, has half the vertices of a runcicantellated 7-cube, t0,1,3{4,35}. Great rhombated hemihepteract (acronym: girhesa)...

Runcinated alternated truncation 19 Runcicantic snub s2,3{p,2q,r} Runcicantellated alternated truncation 20 Snub rectified sr{p,q,2r} [(p,q)+,2r] Alternated...

4+√2) A half-symmetry construction of the runcitruncated 24-cell (or runcicantellated 24-cell), as , also called a runcicantic snub 24-cell, as , has an...

t0,1,3{3,3,3,3,3,3} Runcitruncated 7-simplex 19 t0,2,3{3,3,3,3,3,3} Runcicantellated 7-simplex 20 t1,2,3{3,3,3,3,3,3} Bicantitruncated 7-simplex 21 t0,1...

1,3{3,3,3,3} Runcitruncated 5-simplex (pattix) 13 t0,2,3{3,3,3,3} Runcicantellated 5-simplex (pirx) 14 t0,1,4{3,3,3,3} Steritruncated 5-simplex (cappix)...

Runcitruncated 8-simplex (potane) (0,0,0,0,0,1,1,2,3) 9828 1512 23 t0,2,3 Runcicantellated 8-simplex (prene) (0,0,0,0,0,1,2,2,3) 6804 1512 24 t1,2,3 Bicantitruncated...

heptapeton (Acronym: topal) (Jonathan Bowers) The vertices of the runcicantellated 6-simplex can be most simply positioned in 7-space as permutations...

also be called a runcicantic tesseract with half the vertices of a runcicantellated tesseract with a construction. Bitruncated tesseract/Runcicantic tesseract...

Prismatotruncated hexacontatetrapeton (potag) 24 t0,2,3{3,3,3,3,4} Runcicantellated 6-orthoplex Prismatorhombated hexacontatetrapeton (prog) 25 t1,2,3{3...

runcitruncated 16-cell t0,1,3{3,3,4} runcitruncated tesseract t0,1,3{4,3,3} runcicantellated demitesseract rr{3,31,1} runcitruncated 24-cell t0,1,3{3,4,3} runcitruncated...

Runcitruncated 5-cube Prismatotruncated penteract (pattin) 20 t0,2,3{4,3,3,3} Runcicantellated 5-cube Prismatorhomated penteract (prin) 21 t0,1,4{4,3,3,3} Steritruncated...

3} Runcitruncated 9-simplex 18900 2520 28 t0,2,3{3,3,3,3,3,3,3,3} Runcicantellated 9-simplex 12600 2520 29 t1,2,3{3,3,3,3,3,3,3,3} Bicantitruncated 9-simplex...

3{3,3,3,3,3,3,3} Runcitruncated 8-simplex 23 t0,2,3{3,3,3,3,3,3,3} Runcicantellated 8-simplex 24 t1,2,3{3,3,3,3,3,3,3} Bicantitruncated 8-simplex 25 t0...