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} |
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} |