eight-dimensional geometry, a rectified 8-cube is a convex uniform 8-polytope, being a rectification of the regular 8-cube. There are unique 8 degrees of rectifications...

birectified 6-cube are located in the square face centers of the 6-cube. Rectified hexeract (acronym: rax) (Jonathan Bowers) The rectified 6-cube may be constructed...

centers of the 7-cube. rectified hepteract (Acronym rasa) (Jonathan Bowers) Cartesian coordinates for the vertices of a rectified 7-cube, centered at the origin...

birectified 5-cube are located in the square face centers of the 5-cube. Rectified penteract (acronym: rin) (Jonathan Bowers) The rectified 5-cube may be constructed...

rectified octacross rectified diacosipentacontahexazetton (Acronym: rek) (Jonathan Bowers) There are two Coxeter groups associated with the rectified...

geometry, a rectified 9-cube is a convex uniform 9-polytope, being a rectification of the regular 9-cube. There are 9 rectifications of the 9-cube. The zeroth...

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

geometry, a rectified 10-cube is a convex uniform 10-polytope, being a rectification of the regular 10-cube. There are 10 rectifications of the 10-cube, with...

regular compounds. The cuboctahedron, on the other hand, is a rectified cube or rectified octahedron, and one of only two convex quasiregular polyhedra...

In geometry, the rectified truncated cube is a polyhedron, constructed as a rectified, truncated cube. It has 38 faces: 8 equilateral triangles, 24 isosceles...

6-demicube 6-cube, Rectified 6-cube, Truncated 6-cube, Cantellated 6-cube, Runcinated 6-cube, Stericated 6-cube, Pentellated 6-cube 6-orthoplex, Rectified 6-orthoplex...

convex regular 8-polytopes: {3,3,3,3,3,3,3} - 8-simplex {4,3,3,3,3,3,3} - 8-cube {3,3,3,3,3,3,4} - 8-orthoplex There are no nonconvex regular 8-polytopes....

In geometry, the rectified tesseract, rectified 8-cell is a uniform 4-polytope (4-dimensional polytope) bounded by 24 cells: 8 cuboctahedra, and 16 tetrahedra...

known as rectification, making the cuboctahedron being named the rectified cube and rectified octahedron. An alternative construction is by cutting off all...

envelope is a cube. Two of the truncated cube cells project onto a truncated cube inscribed in the cubical envelope. The other 6 truncated cubes project onto...

makes the dual of rectified 5-orthoplex. The intersection of the 5-cube and 5-orthoplex compound is the uniform birectified 5-cube: = ∩ . The compound...

Cartesian coordinates for the vertices of an 8-demicube centered at the origin are alternate halves of the 8-cube: (±1,±1,±1,±1,±1,±1,±1,±1) with an odd number...

rectified form. New vertices are placed at the center of the edges of the original polygon. Each platonic solid and its dual have the same rectified polyhedron...

rectified 24-cell or rectified icositetrachoron is a uniform 4-dimensional polytope (or uniform 4-polytope), which is bounded by 48 cells: 24 cubes,...

orthoplexes. The rectified 421 can be seen as a rectification of the 421 polytope, creating new vertices on the center of edges of the 421. Rectified...

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...

group orders. The rectified 231 is a rectification of the 231 polytope, creating new vertices on the center of edge of the 231. Rectified...

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

of tetrahedron and icosahedron cells. (The other two are the rectified 5-cell and rectified 600-cell.) Snub icositetrachoron Snub demitesseract Semi-snub...

eight-dimensional geometry, a rectified 8-simplex is a convex uniform 8-polytope, being a rectification of the regular 8-simplex. There are unique 3 degrees...

eight cubes becomes a rhombicuboctahedron in the described way. In addition however, since each cube's edge was previously shared with two other cubes, the...

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...

sequence of honeycombs with square tiling cells: The rectified square tiling honeycomb, t1{4,4,3}, has cube and square tiling facets, with a triangular prism...

semiregular polytope, labeling it as S1 5. Rectified hexateron (Acronym: rix) (Jonathan Bowers) The vertices of the rectified 5-simplex can be more simply positioned...

In geometry, the rectified truncated dodecahedron is a convex polyhedron, constructed as a rectified, truncated dodecahedron. It has 92 faces: 20 equilateral...