| Cantic 6-cube Truncated 6-demicube | |
|---|---|
 D6 Coxeter plane projection | |
| Type | uniform polypeton |
| Schläfli symbol | t0,1{3,33,1} h2{4,34} |
| Coxeter-Dynkin diagram |      =   |
| 5-faces | 76 |
| 4-faces | 636 |
| Cells | 2080 |
| Faces | 3200 |
| Edges | 2160 |
| Vertices | 480 |
| Vertex figure | ( )v[{ }x{3,3}] |
| Coxeter groups | D6, [33,1,1] |
| Properties | convex |
In six-dimensional geometry, a cantic 6-cube (or a truncated 6-demicube) is a uniform 6-polytope.
The Cartesian coordinates for the 480 vertices of a cantic 6-cube centered at the origin and edge length 6√2 are coordinate permutations:
with an odd number of plus signs.
| Coxeter plane | B6 | |
|---|---|---|
| Graph |  | |
| Dihedral symmetry | [12/2] | |
| Coxeter plane | D6 | D5 |
| Graph |  |  |
| Dihedral symmetry | [10] | [8] |
| Coxeter plane | D4 | D3 |
| Graph |  |  |
| Dihedral symmetry | [6] | [4] |
| Coxeter plane | A5 | A3 |
| Graph |  |  |
| Dihedral symmetry | [6] | [4] |
| n | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|
| Symmetry [1+,4,3n-2] | [1+,4,3] = [3,3] | [1+,4,32] = [3,31,1] | [1+,4,33] = [3,32,1] | [1+,4,34] = [3,33,1] | [1+,4,35] = [3,34,1] | [1+,4,36] = [3,35,1] |
| Cantic figure |  |  |  |  |  |  |
| Coxeter | = | = | = | = | = | = |
| Schläfli | h2{4,3} | h2{4,32} | h2{4,33} | h2{4,34} | h2{4,35} | h2{4,36} |
There are 47 uniform polytopes with D6 symmetry, 31 are shared by the B6 symmetry, and 16 are unique:
| D6 polytopes | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
 h{4,34} |  h2{4,34} |  h3{4,34} |  h4{4,34} |  h5{4,34} |  h2,3{4,34} |  h2,4{4,34} |  h2,5{4,34} | ||||
 h3,4{4,34} |  h3,5{4,34} |  h4,5{4,34} |  h2,3,4{4,34} |  h2,3,5{4,34} |  h2,4,5{4,34} |  h3,4,5{4,34} |  h2,3,4,5{4,34} | ||||
In geometry, a truncated tesseract is a uniform 4-polytope formed as the truncation of the regular tesseract.
In five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a 5-hypercube (penteract) with alternated vertices removed.
In geometry, a 6-demicube or demihexeract is a uniform 6-polytope, constructed from a 6-cube (hexeract) with alternated vertices removed. It is part of a dimensionally infinite family of uniform polytopes called demihypercubes.
In geometry, a 10-demicube or demidekeract is a uniform 10-polytope, constructed from the 10-cube with alternated vertices removed. It is part of a dimensionally infinite family of uniform polytopes called demihypercubes.
In six-dimensional geometry, a rectified 6-cube is a convex uniform 6-polytope, being a rectification of the regular 6-cube.
In five-dimensional geometry, a rectified 5-cube is a convex uniform 5-polytope, being a rectification of the regular 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 cantellated 5-cube.
In five-dimensional geometry, a runcinated 5-orthoplex is a convex uniform 5-polytope with 3rd order truncation (runcination) of the regular 5-orthoplex.
In six-dimensional geometry, a runcic 5-cube or is a convex uniform 5-polytope. There are 2 runcic forms for the 5-cube. Runcic 5-cubes have half the vertices of runcinated 5-cubes.
In seven-dimensional geometry, a cantic 7-cube or truncated 7-demicube as a uniform 7-polytope, being a truncation of the 7-demicube.
In eight-dimensional geometry, a cantic 8-cube or truncated 8-demicube is a uniform 8-polytope, being a truncation of the 8-demicube.
In six-dimensional geometry, a runcic 6-cube is a convex uniform 6-polytope. There are 2 unique runcic for the 6-cube.
In six-dimensional geometry, a steric 6-cube is a convex uniform 6-polytope. There are unique 4 steric forms of the 6-cube.
In six-dimensional geometry, a stericated 6-orthoplex is a convex uniform 6-polytope, constructed as a sterication of the regular 6-orthoplex.
In six-dimensional geometry, a pentic 6-cube is a convex uniform 6-polytope.
In seven-dimensional geometry, a runcic 7-cube is a convex uniform 7-polytope, related to the uniform 7-demicube. There are 2 unique forms.
In five-dimensional Euclidean geometry, the quarter 5-cubic honeycomb is a uniform space-filling tessellation. It has half the vertices of the 5-demicubic honeycomb, and a quarter of the vertices of a 5-cube honeycomb. Its facets are 5-demicubes and runcinated 5-demicubes.
In seven-dimensional geometry, a pentic 7-cube is a convex uniform 7-polytope, related to the uniform 7-demicube. There are 8 unique forms.
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.
In seven-dimensional geometry, a stericated 7-cube is a convex uniform 7-polytope, being a runcination of the uniform 7-demicube. There are 4 unique runcinations for the 7-demicube including truncation and cantellation.