Rectified 5-cubes
Appearance
Rectified 5-cube | |
---|---|
Orthogonal projection Projected in B5 Coxeter plane | |
Type | uniform polyteron |
Schläfli symbol | t1{4,3,3,3} |
Coxeter-Dynkin diagrams | |
4-faces | 42 |
Cells | 200 |
Faces | 400 |
Edges | 320 |
Vertices | 80 |
Vertex figure | tetrahedral prism |
Petrie polygon | Decagon |
Coxeter groups | C5, [3,3,3,4] |
Properties | convex |
In five-dimensional geometry, a rectified 5-cube is a uniform 5-polytope, constructed as a rectification of the regular 5-cube.
Alternate names
- Rectified penteract (acronym: rin) (Jonathan Bowers)
Construction
The rectified 5-cube may be constructed from the 5-cube by truncating its vertices at the midpoints of its edges.
Coordinates
The Cartesian coordinates of the vertices of the rectified 5-cube with edge length is given by all permutations of:
Images
Coxeter plane | B5 | B4 / D5 | B3 / D4 / A2 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [10] | [8] | [6] |
Coxeter plane | B2 | A3 | |
Graph | |||
Dihedral symmetry | [4] | [4] |
Related polytopes
This polytope is one of 31 uniform polytera generated from the regular 5-cube or 5-orthoplex.
See also
- Other 5-polytopes:
- 5-simplex - {3,3,3,3}
- 5-cube (penteract) - {4,3,3,3}
- 5-demicube (demipenteract) - {31,2,1}
Notes
External links
- Weisstein, Eric W. "Hypercube". MathWorld.
- Olshevsky, George. "Measure polytope". Glossary for Hyperspace. Archived from the original on 4 February 2007.
- Polytopes of Various Dimensions
- Multi-dimensional Glossary
- Richard Klitzing 5D quasiregulars, (multi)prisms, non-prismatic Wythoffian polyterons o3x3o3o4o - rin