six-dimensional geometry, a runcic 6-cube is a convex uniform 6-polytope. There are 2 unique runcic for the 6-cube. Cantellated 6-demicube/demihexeract Small...

a runcic 5-cube or (runcic 5-demicube, runcihalf 5-cube) is a convex uniform 5-polytope. There are 2 runcic forms for the 5-cube. Runcic 5-cubes have...

reduced to truncated octahedra, and cubes are reduced to truncated tetrahedra. The runcic cubic honeycomb or runcic cubic cellulation is a uniform space-filling...

seven-dimensional geometry, a runcic 7-cube is a convex uniform 7-polytope, related to the uniform 7-demicube. There are 2 unique forms. A runcic 7-cube, h3{4,35}, has...

honeycomb) in Euclidean 3-space made up of cubic cells. It has 4 cubes around every edge, and 8 cubes around each vertex. Its vertex figure is a regular octahedron...

forms: the cantic order-6 cubic honeycomb, h2{4,3,6}, ; the runcic order-6 cubic honeycomb, h3{4,3,6}, ; and the runcicantic order-6 cubic honeycomb, h2,3{4...

the corners. This dissection can also be seen within the runcic cubic honeycomb, with cube, tetrahedron, and rhombicuboctahedron cells. This dissection...

difference can be seen in the vertex figures: A related 4-polytope is the runcic snub 24-cell or prismatorhombisnub icositetrachoron, s3{3,4,3}, . It is...

the vertices of a runcinated tesseract, with its construction, called a runcic tesseract. It has two uniform constructions, as a rectified 8-cell r{4,3...

hyperbolic 3-space. With Schläfli symbol {4,3,5}, it has five cubes {4,3} around each edge, and 20 cubes around each vertex. It is dual with the order-4 dodecahedral...

wedge vertex figure. The runcic order-4 hexagonal tiling honeycomb, ↔ , is composed of triangular tiling, rhombicuboctahedron, cube, and triangular prism...

convex regular 8-polytopes: {3,3,3,3,3,3,3} - 8-simplex {4,3,3,3,3,3,3} - 8-cube {3,3,3,3,3,3,4} - 8-orthoplex There are no nonconvex regular 8-polytopes...

disprismatotesseractihexadecachoron has 16 tetrahedra, 32 cubes, and 32 triangular prisms. Each vertex is shared by 4 cubes, 3 triangular prisms and one tetrahedron....

uniform 6-polytope. The simplest uniform polypeta are regular polytopes: the 6-simplex {3,3,3,3,3}, the 6-cube (hexeract) {4,3,3,3,3}, and the 6-orthoplex...

In 6-dimensional geometry, there are 47 uniform polytopes with D6 symmetry, of which 16 are unique and 31 are shared with the B6 symmetry. There are two...

truncated square tiling, truncated cube, and cuboctahedron facets, with a rectangular pyramid vertex figure. The runcic square tiling honeycomb, h3{4,4,3}...

squares. It can fill space with the truncated cube, truncated tetrahedron and triangular prism as a truncated runcic cubic honeycomb. Truncated small rhombicuboctahedron...

vertex figures, made from 8 cubes and 12 p-gonal prisms at a vertex for any integer p. In the case p = 4, all cells are cubes and the result is the order-5...

Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 Wiley::Kaleidoscopes: Selected Writings of H.S.M. Coxeter (Paper 22) H.S.M...

lower-symmetry construction of the truncated order-4 square tiling honeycomb. The runcic order-4 square tiling honeycomb is a lower-symmetry construction of the...

group [(3,3)+,4]. The truncated octahedral cells become icosahedra. The cubes becomes tetrahedra, and 96 new tetrahedra are created in the gaps from the...

[8] D4 [6] D3 [4] A7 [8] A5 [6] A3 [4] 1 = 8-demicube (hocto) 2 = cantic 8-cube (thocto) 3 = runcic 8-cube 4 = steric 8-cube 5 = pentic 8-cube 6 = hexic...

Regular 6-cube honeycomb, represented by symbols {4,34,4}, B ~ 6 {\displaystyle {\tilde {B}}_{6}} , [31,1,33,4], 95 forms, 64 shared with C ~ 6 {\displaystyle...

Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit...

Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 Wiley::Kaleidoscopes: Selected Writings of H.S.M. Coxeter (Paper 22) H.S.M...

Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit...

are 9 forms, generated by ring permutations of the Coxeter group: There are 6 forms, generated by ring permutations of the Coxeter group: . There are 11...

plain triangular prismatic tilings, respectively, by inserting layers of cubes. Eleven prismatic tilings are obtained by stacking the eleven uniform plane...

such regular polytopes, all convex: {3,3,3,3} - 5-simplex {4,3,3,3} - 5-cube {3,3,3,4} - 5-orthoplex There are no nonconvex regular polytopes in 5 dimensions...

four-dimensional Euclidean geometry, the birectified 16-cell honeycomb (or runcic tesseractic honeycomb) is a uniform space-filling tessellation (or honeycomb)...