5demicube facts for kids
Demipenteract (5demicube) 


Petrie polygon projection 

Type  Uniform 5polytope  
Family (D_{n})  5demicube  
Families (E_{n})  k_{21} polytope 1_{k2} polytope 

Coxeter symbol 
1_{21}  
Schläfli symbols 
{3,3^{2,1}} = h{4,3^{3}} 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{2^{1,1,1,1}} or h{2}h{2}h{2}s{2} 

Coxeter diagrams 
= 

4faces  26  10 {3^{1,1,1}} 16 {3,3,3} 
Cells  120  40 {3^{1,0,1}} 80 {3,3} 
Faces  160  {3} 
Edges  80  
Vertices  16  
Vertex figure 
rectified 5cell 

Petrie polygon 
Octagon  
Symmetry  D_{5}, [3^{2,1,1}] = [1^{+},4,3^{3}] [2^{4}]^{+} 

Properties  convex 
In fivedimensional geometry, a demipenteract or 5demicube is a semiregular 5polytope, constructed from a 5hypercube (penteract) with alternated vertices removed.
It was discovered by Thorold Gosset. Since it was the only semiregular 5polytope (made of more than one type of regular facets), he called it a 5ic semiregular. E. L. Elte identified it in 1912 as a semiregular polytope, labeling it as HM_{5} for a 5dimensional half measure polytope.
Coxeter named this polytope as 1_{21} 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 {3,3^{2,1}}.
It exists in the k_{21} polytope family as 1_{21} with the Gosset polytopes: 2_{21}, 3_{21}, and 4_{21}.
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.
Fundamental convex regular and uniform polytopes in dimensions 2–10  

Family  A_{n}  B_{n}  I_{2}(p) / D_{n}  E_{6} / E_{7} / E_{8} / F_{4} / G_{2}  H_{n}  
Regular polygon  Triangle  Square  pgon  Hexagon  Pentagon  
Uniform polyhedron  Tetrahedron  Octahedron • Cube  Demicube  Dodecahedron • Icosahedron  
Uniform 4polytope  5cell  16cell • Tesseract  Demitesseract  24cell  120cell • 600cell  
Uniform 5polytope  5simplex  5orthoplex • 5cube  5demicube  
Uniform 6polytope  6simplex  6orthoplex • 6cube  6demicube  1_{22} • 2_{21}  
Uniform 7polytope  7simplex  7orthoplex • 7cube  7demicube  1_{32} • 2_{31} • 3_{21}  
Uniform 8polytope  8simplex  8orthoplex • 8cube  8demicube  1_{42} • 2_{41} • 4_{21}  
Uniform 9polytope  9simplex  9orthoplex • 9cube  9demicube  
Uniform 10polytope  10simplex  10orthoplex • 10cube  10demicube  
Uniform npolytope  nsimplex  northoplex • ncube  ndemicube  1_{k2} • 2_{k1} • k_{21}  npentagonal polytope  
Topics: Polytope families • Regular polytope • List of regular polytopes and compounds 