six-dimensional geometry, a runcinated 6-cube is a convex uniform 6-polytope with 3rd order truncations (runcination) of the regular 6-cube. There are 12 unique...

six-dimensional geometry, a runcinated 6-orthplex is a convex uniform 6-polytope with 3rd order truncations (runcination) of the regular 6-orthoplex. There are...

Runcinated 5-simplex, Stericated 5-simplex 5-demicube, Truncated 5-demicube, Cantellated 5-demicube, Runcinated 5-demicube 5-cube, Rectified 5-cube,...

In four-dimensional geometry, a runcinated tesseract (or runcinated 16-cell) is a convex uniform 4-polytope, being a runcination (a 3rd order truncation)...

geometry, a steric 6-cube is a convex uniform 6-polytope. There are unique 4 steric forms of the 6-cube. Runcinated demihexeract/6-demicube Small prismated...

seven-dimensional geometry, a runcinated 7-cube is a convex uniform 7-polytope with 3rd order truncations (runcination) of the regular 7-cube. There are 16 unique...

7-demicube, Runcinated 7-demicube, Stericated 7-demicube, Pentellated 7-demicube 7-cube, Rectified 7-cube, Truncated 7-cube, Cantellated 7-cube, Runcinated 7-cube...

five-dimensional geometry, a runcinated 5-cube is a convex uniform 5-polytope that is a runcination (a 3rd order truncation) of the regular 5-cube. There are 8 unique...

six-dimensional geometry, a runcinated 6-simplex is a convex uniform 6-polytope constructed as a runcination (3rd order truncations) of the regular 6-simplex. There...

figure. The runcinated order-6 cubic honeycomb is the same as the runcinated order-4 hexagonal tiling honeycomb. The runcitruncated order-6 cubic honeycomb...

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...

cubic honeycomb, tr{4,3,4}: The runcinated order-5 cubic honeycomb or runcinated order-4 dodecahedral honeycomb , has cube, dodecahedron, and pentagonal...

in 1912 as a semiregular polytope. Runcinated 24-cell (Norman W. Johnson) Runcinated icositetrachoron Runcinated polyoctahedron Small prismatotetracontoctachoron...

tesseractic cupolae and a runcinated tesseract between them. This dissection can be seen as analogous to the 4D runcinated tesseract being dissected into...

identified it in 1912 as a semiregular polytope. Runcinated 5-cell (Norman Johnson) Runcinated pentachoron Runcinated 4-simplex Expanded 5-cell/4-simplex/pentachoron...

5-cube. Steric 5-cubes have half the vertices of stericated 5-cubes. Steric penteract, runcinated demipenteract Small prismated hemipenteract (siphin) (Jonathan...

In seven-dimensional geometry, a stericated 7-cube (or runcinated 7-demicube) is a convex uniform 7-polytope, being a runcination of the uniform 7-demicube...

runcic forms for the 5-cube. Runcic 5-cubes have half the vertices of runcinated 5-cubes. Cantellated 5-demicube/demipenteract Small rhombated hemipenteract...

In 6-dimensional geometry, there are 64 uniform polytopes with B6 symmetry. There are two regular forms, the 6-orthoplex, and 6-cube with 12 and 64 vertices...

In four-dimensional geometry, a runcinated 120-cell (or runcinated 600-cell) is a convex uniform 4-polytope, being a runcination (a 3rd order truncation)...

dissected cube, using 4 vertices and the center. Four cells exist around 6 edges, and 3 cells around 3 edges. It is related to the runcinated cubic honeycomb...

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...

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...

unique forms. A runcic 7-cube, h3{4,35}, has half the vertices of a runcinated 7-cube, t0,3{4,35}. Small rhombated hemihepteract (Acronym sirhesa) (Jonathan...

has truncated octahedron, cube, and truncated trihexagonal tiling cells, with a mirrored sphenoid vertex figure. The runcinated order-4 hexagonal tiling...

and cantellations. Runcinated hexateron Small prismated hexateron (Acronym: spix) (Jonathan Bowers) The vertices of the runcinated 5-simplex can be most...

has truncated cube, truncated square tiling, and triangular prism facets, with an isosceles triangular pyramid vertex figure. The runcinated square tiling...

In seven-dimensional geometry, a runcinated 7-orthoplex is a convex uniform 7-polytope with 3rd order truncations (runcination) of the regular 7-orthoplex...

Runcinated enneazetton Small prismated enneazetton (Acronym: spene) (Jonathan Bowers) The Cartesian coordinates of the vertices of the runcinated 8-simplex...

runcinated 24-cell, and runcitruncated 24-cell all have 240 cells, while the rectified 24-cell and truncated 24-cell have 240 faces. The runcinated 5-cell...