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...

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

runcinations of the 5-orthoplex with permutations of truncations, and cantellations. Four are more simply constructed relative to the 5-cube. Runcinated pentacross...

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...

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

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...

six-dimensional geometry, a runcinated 5-simplex is a convex uniform 5-polytope with 3rd order truncations (Runcination) of the regular 5-simplex. There are 4...

Cantellated 24-cell, Runcinated 24-cell, Snub 24-cell Rectified 120-cell, Truncated 120-cell, Cantellated 120-cell, Runcinated 120-cell Rectified 600-cell...

hyperspace, George Olshevsky. Polytopes of Various Dimensions, Jonathan Bowers Runcinated uniform polytera (spid), Jonathan Bowers Multi-dimensional Glossary...

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

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

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...

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

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 or above. Unsolved...

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

hypercube honeycomb of Euclidean 5-space, the 5-cube honeycomb, with symbols {4,33,4}, = B ~ 5 {\displaystyle {\tilde {B}}_{5}} There are 47 uniform honeycombs...

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...

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...

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

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)...

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 cubic honeycomb...

hyperplane is a runcinated 5-cell. This cross-section divides the stericated hexateron into two pentachoral hypercupolas consisting of 6 5-cells, 15 tetrahedral...

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

and filling in new faces in the gaps for each opened vertex and edge. Runcinated 4-polytopes/honeycombs forms: Uniform polyhedron Uniform 4-polytope Rectification...

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

runcinated 5-cell. The disphenoidal 30-cell is the dual of the bitruncated 5-cell. It is a 4-dimensional polytope (or polychoron) derived from the 5-cell...

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...

is cell-transitive, consisting of 48 truncated cubes, and also edge-transitive, with 3 truncated cubes cells per edge and with one triangle and two octagons...

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

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...