5-demicube
In five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a 5-hypercube (penteract) with alternated vertices removed.
| Demipenteract (5-demicube) | ||
|---|---|---|
Petrie polygon projection | ||
| Type | Uniform 5-polytope | |
| Family (Dn) | 5-demicube | |
| Families (En) | k21 polytope 1k2 polytope | |
| Coxeter symbol |
121 | |
| Schläfli symbols |
{3,32,1} = h{4,33} s{2,4,3,3} or h{2}h{4,3,3} sr{2,2,4,3} or h{2}h{2}h{4,3} h{2}h{2}h{2}h{4} s{21,1,1,1} or h{2}h{2}h{2}s{2} | |
| Coxeter diagrams |
= | |
| 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 | D5, [32,1,1] = [1+,4,33] [24]+ | |
| Properties | convex | |
It was discovered by Thorold Gosset. Since it was the only semiregular 5-polytope (made of more than one type of regular facets), he called it a 5-ic semi-regular. E. L. Elte identified it in 1912 as a semiregular polytope, labeling it as HM5 for a 5-dimensional half measure polytope.
Coxeter named this polytope as 121 from its Coxeter diagram, which has branches of length 2, 1 and 1 with a ringed node on one of the short branches, and Schläfli symbol or {3,32,1}.
It exists in the k21 polytope family as 121 with the Gosset polytopes: 221, 321, and 421.
The graph formed by the vertices and edges of the demipenteract is sometimes called the Clebsch graph, though that name sometimes refers to the folded cube graph of order five instead.