seven-dimensional geometry, a pentellated 7-cube is a convex uniform 7-polytope with 5th order truncations (pentellation) of the regular 7-cube. There are 32 unique...

In seven-dimensional geometry, a hexic 7-cube is a convex uniform 7-polytope, constructed from the uniform 7-demicube. There are 16 unique forms. The...

constructed from the 6-orthoplex given at pentellated 6-orthoplex. Pentellated 6-orthoplex Expanded 6-cube, expanded 6-orthoplex Small teri-hexeractihexacontitetrapeton...

seven-dimensional geometry, a pentellated 7-orthoplex is a convex uniform 7-polytope with 5th order truncations (pentellation) of the regular 7-orthoplex. There are...

seven-dimensional geometry, a pentellated 7-simplex is a convex uniform 7-polytope with 5th order truncations (pentellation) of the regular 7-simplex. There are...

Rectified 7-cube, 7-cube, Truncated 7-cube, Cantellated 7-cube, Runcinated 7-cube, Stericated 7-cube, Pentellated 7-cube, Hexicated 7-cube 7-orthoplex...

other 6 more easily constructed as a pentellated 6-cube. The simple pentellated 6-orthoplex (Same as pentellated 5-cube) is also called an expanded 6-orthoplex...

Rectified 7-cube, Truncated 7-cube, Cantellated 7-cube, Runcinated 7-cube, Stericated 7-cube, Pentellated 7-cube, Hexicated 7-cube 7-orthoplex, Rectified 7-orthoplex...

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...

In 7-dimensional geometry, there are 128 uniform polytopes with B7 symmetry. There are two regular forms, the 7-orthoplex, and 8-cube with 14 and 128 vertices...

cross-section of the pentellated 6-simplex with a 5-dimensional hyperplane is a stericated hexateron. This cross-section divides the pentellated 6-simplex into...

6-cube is a convex uniform 6-polytope. There are 8 pentic forms of the 6-cube. The pentic 6-cube, , has half of the vertices of a pentellated 6-cube, ...

{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...

honeycomb, and a quarter of the vertices of a 7-cube honeycomb. Its facets are 7-demicubes, pentellated 7-demicubes, and {31,1,1}×{3,3} duoprisms. This...

the pentellated 8-simplex, while the bipentellated 8-simple is doubled to [18] symmetry. The Cartesian coordinates of the vertices of the pentellated 8-simplex...

The movement of the analog stick(s) of the Nintendo 64 controller, the GameCube controller, the Wii Nunchuk and the Classic Controller is restricted by a...

polytopes with B6 symmetry. There are two regular forms, the 6-orthoplex, and 6-cube with 12 and 64 vertices respectively. The 6-demicube is added with half the...

10-polytopes: {3,3,3,3,3,3,3,3,3} - 10-simplex {4,3,3,3,3,3,3,3,3} - 10-cube {3,3,3,3,3,3,3,3,4} - 10-orthoplex There are no nonconvex regular 10-polytopes...

polytopes with B8 symmetry. There are two regular forms, the 8-orthoplex and 8-cube, with 16 and 256 vertices respectively. The 8-demicube is added with half...

In 7-dimensional geometry, there are 71 uniform polytopes with A7 symmetry. There is one self-dual regular form, the 7-simplex with 8 vertices. Each can...

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...

with A6 symmetry. There is one self-dual regular form, the 6-simplex with 7 vertices. Each can be visualized as symmetric orthographic projections in...

regular 9-polytopes: {3,3,3,3,3,3,3,3} - 9-simplex {4,3,3,3,3,3,3,3} - 9-cube {3,3,3,3,3,3,3,4} - 9-orthoplex There are no nonconvex regular 9-polytopes...

planes. Ak has [k+1] symmetry. These 135 polytopes are each shown in these 7 symmetry planes, with vertices and edges drawn, and vertices colored by the...