| Demipenteract (5-demicube) |
||
|---|---|---|
Petrie polygon projection |
||
| Type | Uniform 5-polytope | |
| Family (Dn) | 5-demicube | |
| Families (En) | k21 polytope 1k2 polytope |
|
| Coxeter symbol | 121 | |
| Schläfli symbol | {31,2,1} h{4,3,3,3} s{2,2,2,2} |
|
| Coxeter-Dynkin diagram | ||
| 4-faces | 26 | 10 {31,1,1} 16 {3,3,3} |
| Cells | 120 | 40 {31,0,1} 80 {3,3} |
| Faces | 160 | {3} |
| Edges | 80 | |
| Vertices | 16 | |
| Vertex figure | rectified 5-cell |
|
| Petrie polygon | Octagon | |
| Symmetry group | D5, [34,1,1] = [1+,4,33] [24]+ |
|
| Properties | convex | |
In five dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a 5-hypercube (penteract) with alternated vertices deleted.
It was discovered by Thorold Gosset. Since it was the only semiregular 5-polytope (made of more than one type of regular hypercell), he called it a 5-ic semi-regular.
Coxeter named this polytope as 121 from its Coxeter-Dynkin diagram, which has branches of length 2, 1 and 1 with a ringed node on one of the short branches. It exists in the k21 polytope family as 121 with the Gosset polytopes: 221, 321, and 421.
Contents |
Cartesian coordinates for the vertices of a demipenteract centered at the origin and edge length 2√2 are alternate halves of the penteract:
with an odd number of plus signs.
Perspective projection. |
| Coxeter plane | B5 | |
|---|---|---|
| Graph | ||
| Dihedral symmetry | [10/2] | |
| Coxeter plane | D5 | D4 |
| Graph | ||
| Dihedral symmetry | [8] | [6] |
| Coxeter plane | D3 | A3 |
| Graph | ||
| Dihedral symmetry | [4] | [4] |
It is a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.
There are 23 uniform polytera (uniform 5-polytope) that can be constructed from the D5 symmetry of the demipenteract, 8 of which are unique to this family, and 15 are shared within the penteractic family.
t0(121) |
t0,1(121) |
t0,2(121) |
t0,3(121) |
t0,1,2(121) |
t0,1,3(121) |
t0,2,3(121) |
t0,1,2,3(121) |