7-demicube (half 7-cube, h{4,35}) |
Pentic 7-cube h5{4,35} |
Penticantic 7-cube h2,5{4,35} |
Pentiruncic 7-cube h3,5{4,35} |
Pentiruncicantic 7-cube h2,3,5{4,35} |
Pentisteric 7-cube h4,5{4,35} |
Pentistericantic 7-cube h2,4,5{4,35} |
Pentisteriruncic 7-cube h3,4,5{4,35} |
Penticsteriruncicantic 7-cube h2,3,4,5{4,35} |
Orthogonal projections in D7 Coxeter plane |
---|
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.
Pentic 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,4{3,34,1} h5{4,35} |
Coxeter-Dynkin diagram | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 13440 |
Vertices | 1344 |
Vertex figure | |
Coxeter groups | D7, [34,1,1] |
Properties | convex |
The Cartesian coordinates for the vertices of a pentic 7-cube centered at the origin are coordinate permutations:
with an odd number of plus signs.
Coxeter plane |
B7 | D7 | D6 |
---|---|---|---|
Graph | |||
Dihedral symmetry |
[14/2] | [12] | [10] |
Coxeter plane | D5 | D4 | D3 |
Graph | |||
Dihedral symmetry |
[8] | [6] | [4] |
Coxeter plane |
A5 | A3 | |
Graph | |||
Dihedral symmetry |
[6] | [4] |
Dimensional family of pentic n-cubes | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
n | 6 | 7 | 8 | ||||||||
[1+,4,3n-2 = [3,3n-3,1] |
[1+,4,34 = [3,33,1] |
[1+,4,35 = [3,34,1] |
[1+,4,36 = [3,35,1] | ||||||||
Cantic figure |
|||||||||||
Coxeter | = |
= |
= | ||||||||
Schläfli | h5{4,34} | h5{4,35} | h5{4,36} |
Coxeter plane |
B7 | D7 | D6 |
---|---|---|---|
Graph | |||
Dihedral symmetry |
[14/2] | [12] | [10] |
Coxeter plane | D5 | D4 | D3 |
Graph | |||
Dihedral symmetry |
[8] | [6] | [4] |
Coxeter plane |
A5 | A3 | |
Graph | |||
Dihedral symmetry |
[6] | [4] |
Coxeter plane |
B7 | D7 | D6 |
---|---|---|---|
Graph | |||
Dihedral symmetry |
[14/2] | [12] | [10] |
Coxeter plane | D5 | D4 | D3 |
Graph | |||
Dihedral symmetry |
[8] | [6] | [4] |
Coxeter plane |
A5 | A3 | |
Graph | |||
Dihedral symmetry |
[6] | [4] |
Coxeter plane |
B7 | D7 | D6 |
---|---|---|---|
Graph | |||
Dihedral symmetry |
[14/2] | [12] | [10] |
Coxeter plane | D5 | D4 | D3 |
Graph | |||
Dihedral symmetry |
[8] | [6] | [4] |
Coxeter plane |
A5 | A3 | |
Graph | |||
Dihedral symmetry |
[6] | [4] |
Coxeter plane |
B7 | D7 | D6 |
---|---|---|---|
Graph | |||
Dihedral symmetry |
[14/2] | [12] | [10] |
Coxeter plane | D5 | D4 | D3 |
Graph | |||
Dihedral symmetry |
[8] | [6] | [4] |
Coxeter plane |
A5 | A3 | |
Graph | |||
Dihedral symmetry |
[6] | [4] |
Coxeter plane |
B7 | D7 | D6 |
---|---|---|---|
Graph | |||
Dihedral symmetry |
[14/2] | [12] | [10] |
Coxeter plane | D5 | D4 | D3 |
Graph | |||
Dihedral symmetry |
[8] | [6] | [4] |
Coxeter plane |
A5 | A3 | |
Graph | |||
Dihedral symmetry |
[6] | [4] |
Coxeter plane |
B7 | D7 | D6 |
---|---|---|---|
Graph | |||
Dihedral symmetry |
[14/2] | [12] | [10] |
Coxeter plane | D5 | D4 | D3 |
Graph | |||
Dihedral symmetry |
[8] | [6] | [4] |
Coxeter plane |
A5 | A3 | |
Graph | |||
Dihedral symmetry |
[6] | [4] |
Coxeter plane |
B7 | D7 | D6 |
---|---|---|---|
Graph | |||
Dihedral symmetry |
[14/2] | [12] | [10] |
Coxeter plane | D5 | D4 | D3 |
Graph | |||
Dihedral symmetry |
[8] | [6] | [4] |
Coxeter plane |
A5 | A3 | |
Graph | |||
Dihedral symmetry |
[6] | [4] |
This polytope is based on the 7-demicube, a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.
There are 95 uniform polytopes with D7 symmetry, 63 are shared by the BC7 symmetry, and 32 are unique:
7-demicube (half 7-cube, h{4,35}) |
Pentic 7-cube h5{4,35} |
Penticantic 7-cube h2,5{4,35} |
Pentiruncic 7-cube h3,5{4,35} |
Pentiruncicantic 7-cube h2,3,5{4,35} |
Pentisteric 7-cube h4,5{4,35} |
Pentistericantic 7-cube h2,4,5{4,35} |
Pentisteriruncic 7-cube h3,4,5{4,35} |
Penticsteriruncicantic 7-cube h2,3,4,5{4,35} |
Orthogonal projections in D7 Coxeter plane |
---|
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.
Pentic 7-cube | |
---|---|
Type | uniform 7-polytope |
Schläfli symbol | t0,4{3,34,1} h5{4,35} |
Coxeter-Dynkin diagram | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 13440 |
Vertices | 1344 |
Vertex figure | |
Coxeter groups | D7, [34,1,1] |
Properties | convex |
The Cartesian coordinates for the vertices of a pentic 7-cube centered at the origin are coordinate permutations:
with an odd number of plus signs.
Coxeter plane |
B7 | D7 | D6 |
---|---|---|---|
Graph | |||
Dihedral symmetry |
[14/2] | [12] | [10] |
Coxeter plane | D5 | D4 | D3 |
Graph | |||
Dihedral symmetry |
[8] | [6] | [4] |
Coxeter plane |
A5 | A3 | |
Graph | |||
Dihedral symmetry |
[6] | [4] |
Dimensional family of pentic n-cubes | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
n | 6 | 7 | 8 | ||||||||
[1+,4,3n-2 = [3,3n-3,1] |
[1+,4,34 = [3,33,1] |
[1+,4,35 = [3,34,1] |
[1+,4,36 = [3,35,1] | ||||||||
Cantic figure |
|||||||||||
Coxeter | = |
= |
= | ||||||||
Schläfli | h5{4,34} | h5{4,35} | h5{4,36} |
Coxeter plane |
B7 | D7 | D6 |
---|---|---|---|
Graph | |||
Dihedral symmetry |
[14/2] | [12] | [10] |
Coxeter plane | D5 | D4 | D3 |
Graph | |||
Dihedral symmetry |
[8] | [6] | [4] |
Coxeter plane |
A5 | A3 | |
Graph | |||
Dihedral symmetry |
[6] | [4] |
Coxeter plane |
B7 | D7 | D6 |
---|---|---|---|
Graph | |||
Dihedral symmetry |
[14/2] | [12] | [10] |
Coxeter plane | D5 | D4 | D3 |
Graph | |||
Dihedral symmetry |
[8] | [6] | [4] |
Coxeter plane |
A5 | A3 | |
Graph | |||
Dihedral symmetry |
[6] | [4] |
Coxeter plane |
B7 | D7 | D6 |
---|---|---|---|
Graph | |||
Dihedral symmetry |
[14/2] | [12] | [10] |
Coxeter plane | D5 | D4 | D3 |
Graph | |||
Dihedral symmetry |
[8] | [6] | [4] |
Coxeter plane |
A5 | A3 | |
Graph | |||
Dihedral symmetry |
[6] | [4] |
Coxeter plane |
B7 | D7 | D6 |
---|---|---|---|
Graph | |||
Dihedral symmetry |
[14/2] | [12] | [10] |
Coxeter plane | D5 | D4 | D3 |
Graph | |||
Dihedral symmetry |
[8] | [6] | [4] |
Coxeter plane |
A5 | A3 | |
Graph | |||
Dihedral symmetry |
[6] | [4] |
Coxeter plane |
B7 | D7 | D6 |
---|---|---|---|
Graph | |||
Dihedral symmetry |
[14/2] | [12] | [10] |
Coxeter plane | D5 | D4 | D3 |
Graph | |||
Dihedral symmetry |
[8] | [6] | [4] |
Coxeter plane |
A5 | A3 | |
Graph | |||
Dihedral symmetry |
[6] | [4] |
Coxeter plane |
B7 | D7 | D6 |
---|---|---|---|
Graph | |||
Dihedral symmetry |
[14/2] | [12] | [10] |
Coxeter plane | D5 | D4 | D3 |
Graph | |||
Dihedral symmetry |
[8] | [6] | [4] |
Coxeter plane |
A5 | A3 | |
Graph | |||
Dihedral symmetry |
[6] | [4] |
Coxeter plane |
B7 | D7 | D6 |
---|---|---|---|
Graph | |||
Dihedral symmetry |
[14/2] | [12] | [10] |
Coxeter plane | D5 | D4 | D3 |
Graph | |||
Dihedral symmetry |
[8] | [6] | [4] |
Coxeter plane |
A5 | A3 | |
Graph | |||
Dihedral symmetry |
[6] | [4] |
This polytope is based on the 7-demicube, a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.
There are 95 uniform polytopes with D7 symmetry, 63 are shared by the BC7 symmetry, and 32 are unique: