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...

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...

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...

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

In 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...

{3[8]} C ~ 7 {\displaystyle {\tilde {C}}_{7}} 135 uniquely ringed forms, including: Regular 7-cube honeycomb: {4,34,4} = {4,34,31,1}, = B ~ 7 {\displaystyle...

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

convex regular 7-polytopes: {3,3,3,3,3,3} - 7-simplex {4,3,3,3,3,3} - 7-cube {3,3,3,3,3,4} - 7-orthoplex There are no nonconvex regular 7-polytopes. The...

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...

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...

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

In 7-dimensional geometry, there are 95 uniform polytopes with D7 symmetry; 32 are unique, and 63 are shared with the B7 symmetry. There are two regular...

[8] B3 [6]+ B2 [4] Octahedron centered Dual octahedron centered Octahedron centered 10 snub 24-cell s{3,4,3} 11 Nonuniform runcic snub 24-cell s3{3,4,3}...

Cantic 5-cube Truncated hemipenteract (thin) 3 = h3{4,3,3,3} Runcic 5-cube Small rhombated hemipenteract (sirhin) 4 = h4{4,3,3,3} Steric 5-cube Small prismated...

8-demicube (hocto) 2 = cantic 8-cube (thocto) 3 = runcic 8-cube 4 = steric 8-cube 5 = pentic 8-cube 6 = hexic 8-cube 7 = heptic 8-cube 8 = 9 = 10 = 11 = 12 = 13...

In 4-dimensional geometry, there are 7 uniform 4-polytopes with reflections of D4 symmetry, all are shared with higher symmetry constructions in the B4...

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...

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...

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

symmetry exists in these polytopes. These 16 polytopes are each shown in these 7 symmetry planes, with vertices and edges drawn, and vertices colored by the...

or . 7 are half symmetry forms of [3,3,6]: ↔ . There are 11 forms, 4 unique, generated by ring permutations of the Coxeter group: [4,3[3]] or . 7 are half...

divided into two subgroups, each with 12 forms, and 7 "middle" forms which equally belong in both. The 5-cube family of 5-polytopes are given by the convex...

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

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 (hexacross) {3,3,3,3,4}. Regular...