5-demicube
5-demicube | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Hin |
Coxeter diagram | x3o3o3o *b3o () |
Elements | |
Tera | 16 pentachora, 10 hexadecachora |
Cells | 40+80 tetrahedra |
Faces | 160 triangles |
Edges | 80 |
Vertices | 16 |
Vertex figure | Rectified pentachoron, edge length 1 |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Hex–tet–pen: |
Hex–tet–hex: 90° | |
Height | |
Central density | 1 |
Number of external pieces | 26 |
Level of complexity | 3 |
Related polytopes | |
Army | Hin |
Regiment | Hin |
Dual | Semistellated triacontaditeron |
Conjugate | None |
Abstract & topological properties | |
Flag count | 5760 |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | D5, order 1920 |
Convex | Yes |
Nature | Tame |
The 5-demicube, also called the hemipenteract, demipenteract or hin, is a convex uniform 5-polytope. It has 10 hexadecachora, and 16 pentachora, as facets, with 5 of each at a vertex forming a rectified pentachoron as the vertex figure. It is the 5-dimensional demihypercube and is formed by alternating the 5-cube.
This is the lowest-dimensional demihypercube that is not identical to another regular polytope of the same dimension.
It is also a convex segmentoteron, as a hexadecachoron atop rotated hexadecachoron, or hexadecachoric alterprism. It is also the digonal-tetrahedral duoantiprism.
Vertex coordinates[edit | edit source]
The vertices of a 5-demicube of edge length 1, centered at the origin, are given by all even sign changes of:
- .
Representations[edit | edit source]
A 5-demicube has the following Coxeter diagrams:
- x3o3o3o *b3o () (full symmetry)
- s4o3o3o3o () (as alternated penteract)
- xo3oo3ox *b3oo&#x (D4 axial, demitesseractic alterprism)
- ooo3oxo3ooo3oox&#xt (A4 axial, vertex-first)
- xox3ooo3oxo oxo&#xt (A3×A1 axial, tetrahedron-first)
- xo3oo3ox xo ox&#zx (A3×A1×A1 symmetry)
- xoxo oxox oxoo3ooxo&#xt (A2×A1×A1 axial, edge-first)
Related polytopes[edit | edit source]
The 5-demicube is the colonel of a 6-member regiment. Its other members include the dishexadecateron, hexadecapenteract, retrodishexadecateron, retropenteractihexadecateron, and the noble hexadecateron.
The hollow stellated icositetrachoric antiprism can be constructed as a blend of 6 demipenteracts.
External links[edit | edit source]
- Bowers, Jonathan. "Category 1: Primary Polytera" (#7).
- Klitzing, Richard. "hin".
- Wikipedia contributors. "5-demicube".