# Category: 5-polytopes

5-cube
In five-dimensional geometry, a 5-cube is a name for a five-dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10 tesseract 4-faces. It is represented by Schläfli s
Cantellated 24-cell honeycomb
In four-dimensional Euclidean geometry, the cantellated 24-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a cantellation of the regular 24-cell honeycomb, containing rectified
Runcicantellated tesseractic honeycomb
In four-dimensional Euclidean geometry, the runcicantellated tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
Steric 5-cubes
In five-dimensional geometry, a steric 5-cube or (steric 5-demicube or sterihalf 5-cube) is a convex uniform 5-polytope. There are unique 4 steric forms of the 5-cube. Steric 5-cubes have half the ver
Rectified 5-simplexes
In five-dimensional geometry, a rectified 5-simplex is a convex uniform 5-polytope, being a rectification of the regular 5-simplex. There are three unique degrees of rectifications, including the zero
5-simplex
In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope. It has six vertices, 15 edges, 20 triangle faces, 15 tetrahedral cells, and 6 5-cell facets. It has a dihedral angle of cos
B5 polytope
In 5-dimensional geometry, there are 31 uniform polytopes with B5 symmetry. There are two regular forms, the 5-orthoplex, and 5-cube with 10 and 32 vertices respectively. The 5-demicube is added as an
Steritruncated tesseractic honeycomb
In four-dimensional Euclidean geometry, the steritruncated tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
Rectified 24-cell honeycomb
In four-dimensional Euclidean geometry, the rectified 24-cell honeycomb is a uniform space-filling honeycomb. It is constructed by a rectification of the regular 24-cell honeycomb, containing tesserac
Truncated 24-cell honeycomb
In four-dimensional Euclidean geometry, the truncated 24-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a truncation of the regular 24-cell honeycomb, containing tesseract and
Truncated 16-cell honeycomb
In four-dimensional Euclidean geometry, the truncated 16-cell honeycomb (or cantic tesseractic honeycomb) is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space. It is constructed
Birectified 16-cell honeycomb
In four-dimensional Euclidean geometry, the birectified 16-cell honeycomb (or runcic tesseractic honeycomb) is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
Steriruncic tesseractic honeycomb
In four-dimensional Euclidean geometry, the steriruncic tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
Runcicantitruncated tesseractic honeycomb
In four-dimensional Euclidean geometry, the runcicantitruncated tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
Truncated 5-cubes
In five-dimensional geometry, a truncated 5-cube is a convex uniform 5-polytope, being a truncation of the regular 5-cube. There are four unique truncations of the 5-cube. Vertices of the truncated 5-
16-cell honeycomb
In four-dimensional Euclidean geometry, the 16-cell honeycomb is one of the three regular space-filling tessellations (or honeycombs), represented by Schläfli symbol {3,3,4,3}, and constructed by a 4-
Steric tesseractic honeycomb
In four-dimensional Euclidean geometry, the steric tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
5-cell honeycomb
In four-dimensional Euclidean geometry, the 4-simplex honeycomb, 5-cell honeycomb or pentachoric-dispentachoric honeycomb is a space-filling tessellation honeycomb. It is composed of 5-cells and recti
Cantellated tesseractic honeycomb
In four-dimensional Euclidean geometry, the cantellated tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space. It is constructed by a cantellation of a tess
Great 120-cell honeycomb
In the geometry of hyperbolic 4-space, the great 120-cell honeycomb is one of four regular star-honeycombs. With Schläfli symbol {5,5/2,5,3}, it has three great 120-cells around each face. It is dual
Runcinated 24-cell honeycomb
In four-dimensional Euclidean geometry, the runcinated 24-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a runcination of the regular 24-cell honeycomb, containing runcinated 2
Stericantellated tesseractic honeycomb
In four-dimensional Euclidean geometry, the stericantellated tesseractic honeycomb is a uniform space-filling honeycomb.
Steriruncitruncated tesseractic honeycomb
In four-dimensional Euclidean geometry, the steriruncitruncated tesseractic honeycomb is a uniform space-filling honeycomb.
Tesseractic honeycomb
In four-dimensional euclidean geometry, the tesseractic honeycomb is one of the three regular space-filling tessellations (or honeycombs), represented by Schläfli symbol {4,3,3,4}, and constructed by
Steriruncicantic tesseractic honeycomb
In four-dimensional Euclidean geometry, the steriruncicantic tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
Steritruncated 16-cell honeycomb
In four-dimensional Euclidean geometry, the steritruncated 16-cell honeycomb is a uniform space-filling honeycomb, with runcinated 24-cell, truncated 16-cell, octahedral prism, 3-6 duoprism, and trunc
Truncated 5-orthoplexes
In five-dimensional geometry, a truncated 5-orthoplex is a convex uniform 5-polytope, being a truncation of the regular 5-orthoplex. There are 4 unique truncations of the 5-orthoplex. Vertices of the
A5 polytope
In 5-dimensional geometry, there are 19 uniform polytopes with A5 symmetry. There is one self-dual regular form, the 5-simplex with 6 vertices. Each can be visualized as symmetric orthographic project
Runcinated 5-simplexes
In 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 unique runcinations of the 5-simplex w
5-demicube
In five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a 5-hypercube (penteract) with alternated vertices removed. It was discovered by Thorold Gosse
24-cell honeycomb
In four-dimensional Euclidean geometry, the 24-cell honeycomb, or icositetrachoric honeycomb is a regular space-filling tessellation (or honeycomb) of 4-dimensional Euclidean space by regular 24-cells
Cantic 5-cube
In geometry of five dimensions or higher, a cantic 5-cube, cantihalf 5-cube, truncated 5-demicube is a uniform 5-polytope, being a truncation of the 5-demicube. It has half the vertices of a cantellat
Order-5 icosahedral 120-cell honeycomb
In the geometry of hyperbolic 4-space, the order-5 icosahedral 120-cell honeycomb is one of four regular star-honeycombs. With Schläfli symbol {3,5,5/2,5}, it has five icosahedral 120-cells around eac
Stericantitruncated 16-cell honeycomb
In four-dimensional Euclidean geometry, the stericantitruncated 16-cell honeycomb is a uniform space-filling honeycomb.
Runcinated 5-cubes
In 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 unique 8 degrees of runcinations of the
Runcinated 5-orthoplexes
In five-dimensional geometry, a runcinated 5-orthoplex is a convex uniform 5-polytope with 3rd order truncation (runcination) of the regular 5-orthoplex. There are 8 runcinations of the 5-orthoplex wi
Cantitruncated tesseractic honeycomb
In four-dimensional Euclidean geometry, the cantitruncated tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
Truncated tesseractic honeycomb
In four-dimensional Euclidean geometry, the truncated tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space. It is constructed by a truncation of a tesserac
5-polytope
In geometry, a five-dimensional polytope (or 5-polytope) is a polytope in five-dimensional space, bounded by (4-polytope) facets, pairs of which share a polyhedral cell.
Runcic 5-cubes
In six-dimensional geometry, 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 half the vertices of
Cantellated 5-orthoplexes
In five-dimensional geometry, a cantellated 5-orthoplex is a convex uniform 5-polytope, being a cantellation of the regular 5-orthoplex. There are 6 cantellation for the 5-orthoplex, including truncat
Bitruncated 24-cell honeycomb
In four-dimensional Euclidean geometry, the bitruncated 24-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a bitruncation of the regular 24-cell honeycomb, constructed by trunca
Uniform 5-polytope
In geometry, a uniform 5-polytope is a five-dimensional uniform polytope. By definition, a uniform 5-polytope is vertex-transitive and constructed from uniform 4-polytope facets. The complete set of c
Runcinated 16-cell honeycomb
In four-dimensional Euclidean geometry, the runcinated 16-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a runcination of the regular 16-cell honeycomb, containing Rectified 24
Stericated 5-cubes
In five-dimensional geometry, a stericated 5-cube is a convex uniform 5-polytope with fourth-order truncations (sterication) of the regular 5-cube. There are eight degrees of sterication for the 5-cub
Omnitruncated tesseractic honeycomb
In four-dimensional Euclidean geometry, the omnitruncated tesseractic honeycomb is a uniform space-filling honeycomb. It has omnitruncated tesseract, truncated cuboctahedral prism, and 8-8 duoprism fa
Stericated 24-cell honeycomb
In four-dimensional Euclidean geometry, the stericated 24-cell honeycomb (or stericated 16-cell honeycomb) is a uniform space-filling honeycomb. It can be seen as a sterication of the regular 24-cell
Snub 24-cell honeycomb
In four-dimensional Euclidean geometry, the snub 24-cell honeycomb, or snub icositetrachoric honeycomb is a uniform space-filling tessellation (or honeycomb) by snub 24-cells, 16-cells, and 5-cells. I
Stericated 5-simplexes
In five-dimensional geometry, a stericated 5-simplex is a convex uniform 5-polytope with fourth-order truncations (sterication) of the regular 5-simplex. There are six unique sterications of the 5-sim
Rectified 5-cubes
In five-dimensional geometry, a rectified 5-cube is a convex uniform 5-polytope, being a rectification of the regular 5-cube. There are 5 degrees of rectifications of a 5-polytope, the zeroth here bei
Small stellated 120-cell honeycomb
In the geometry of hyperbolic 4-space, the small stellated 120-cell honeycomb is one of four regular star-honeycombs. With Schläfli symbol {5/2,5,3,3}, it has three small stellated 120-cells around ea
Runcicantellated 24-cell honeycomb
In four-dimensional Euclidean geometry, the runcicantellated 24-cell honeycomb is a uniform space-filling honeycomb.
Cantellated 5-cubes
In six-dimensional geometry, a cantellated 5-cube is a convex uniform 5-polytope, being a cantellation of the regular 5-cube. There are 6 unique cantellation for the 5-cube, including truncations. Hal
Truncated 5-simplexes
In five-dimensional geometry, a truncated 5-simplex is a convex uniform 5-polytope, being a truncation of the regular 5-simplex. There are unique 2 degrees of truncation. Vertices of the truncation 5-
5-orthoplex
In five-dimensional geometry, a 5-orthoplex, or 5-cross polytope, is a five-dimensional polytope with 10 vertices, 40 edges, 80 triangle faces, 80 tetrahedron cells, 32 5-cell 4-faces. It has two cons
Pentagrammic-order 600-cell honeycomb
In the geometry of hyperbolic 4-space, the pentagrammic-order 600-cell honeycomb is one of four regular star-honeycombs. With Schläfli symbol {3,3,5,5/2}, it has five 600-cells around each face in a p
Stericantic tesseractic honeycomb
In four-dimensional Euclidean geometry, the stericantic tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
Rectified 5-orthoplexes
In five-dimensional geometry, a rectified 5-orthoplex is a convex uniform 5-polytope, being a rectification of the regular 5-orthoplex. There are 5 degrees of rectifications for any 5-polytope, the ze
Bitruncated 16-cell honeycomb
In four-dimensional Euclidean geometry, the bitruncated 16-cell honeycomb (or runcicantic tesseractic honeycomb) is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
Cantitruncated 24-cell honeycomb
In four-dimensional Euclidean geometry, the cantitruncated 24-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a cantitruncation of the regular 24-cell honeycomb, containing trun
Runcitruncated tesseractic honeycomb
In four-dimensional Euclidean geometry, the runcitruncated tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
Bitruncated tesseractic honeycomb
In four-dimensional Euclidean geometry, the bitruncated tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space. It is constructed by a bitruncation of a tess
D5 polytope
In 5-dimensional geometry, there are 23 uniform polytopes with D5 symmetry, 8 are unique, and 15 are shared with the B5 symmetry. There are two special forms, the 5-orthoplex, and 5-demicube with 10 a
Rectified tesseractic honeycomb
In four-dimensional Euclidean geometry, the rectified tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space. It is constructed by a rectification of a tesse
Cantellated 5-simplexes
In five-dimensional geometry, a cantellated 5-simplex is a convex uniform 5-polytope, being a cantellation of the regular 5-simplex. There are unique 4 degrees of cantellation for the 5-simplex, inclu
Runcinated tesseractic honeycomb
In four-dimensional Euclidean geometry, the runcinated tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space. It is constructed by a runcination of a tesser
Stericantitruncated tesseractic honeycomb
In four-dimensional Euclidean geometry, the stericantitruncated tesseractic honeycomb is a uniform space-filling honeycomb. It is composed of runcitruncated 16-cell, cantitruncated tesseract, rhombicu