Demicube
n -demicube | |
---|---|
Rank | n |
Type | Uniform |
Notation | |
Coxeter diagram | ... |
Elements | |
Vertices | |
Vertex figure | Rectified (n -1)-simplex, edge length 1 |
Measures (edge length 1) | |
Circumradius | |
Volume | |
Dihedral angles | Demicube-demicube-demicube: 90° |
Demicube-simplex-simplex: | |
Height | |
Central density | 1 |
Number of external pieces | |
Level of complexity | |
Related polytopes | |
Conjugate | None |
Abstract & topological properties | |
Flag count | |
Euler characteristic | 0 if n even 2 if n odd |
Orientable | Yes |
Properties | |
Symmetry | Dn , order |
Convex | Yes |
Nature | Tame |
A demicube, demihypercube, or half measure polytope is one of an infinite family of convex uniform polytopes. The n -dimensional demicube, or simply the n -demicube, has vertices. It can be formed by alternation of the n -hypercube, making its facets into (n -1)-demicube facets and half of its vertex figures into (n -1)-simplex facets.
Examples[edit | edit source]
The demicubes up to 10D are the following:
Rank | Name | Picture | Rank | Name | Picture | |
---|---|---|---|---|---|---|
3 | Tetrahedron | 7 | Demihepteract | |||
4 | Hexadecachoron | 8 | Demiocteract | |||
5 | Demipenteract | 9 | Demienneract | |||
6 | Demihexeract | 10 | Demidekeract |
Vertex coordinates[edit | edit source]
Coordinates for the vertices of an n -demicube with edge length 1 are given by all even sign changes of:
- (√2/4, √2/4, ..., √2/4).
Measures[edit | edit source]
- The circumradius of an n -demicube of unit edge length is .
- Its height from a demicube facet to the opposite demicube facet is , regardless of n .
- The angle between two demicube facet hyperplanes is 90°, and the angle between a demicube and a simplex facet hyperplane is .
External links[edit | edit source]
- Wikipedia contributors. "Demihypercube".
- Klitzing, Richard. Demihypercube Dn