Retroantiprismatosnub disicositetrachoron
Retroantiprismatosnub disicositetrachoron | |
---|---|
Rank | 4 |
Type | Uniform |
Notation | |
Bowers style acronym | Rappisdi |
Elements | |
Cells | 96 octahedra, 24 icosahedra, 24 great icosahedra |
Faces | 96+192+288+288 triangles |
Edges | 144+576 |
Vertices | 96 |
Vertex figure | Disrhombitritrihedron, edge length 1 |
Measures (edge length 1) | |
Circumradius | 1 |
Hypervolume | |
Dichoral angles | Gike–3–oct: |
Oct–3–oct: 120° | |
Gike–3–ike: 60° | |
Ike–3–oct: | |
Number of external pieces | 6552 |
Level of complexity | 571 |
Related polytopes | |
Army | Sadi |
Regiment | Rappisdi |
Conjugate | Retroantiprismatosnub disicositetrachoron |
Convex core | Icositetrachoron |
Abstract & topological properties | |
Euler characteristic | 96 |
Orientable | Yes |
Properties | |
Symmetry | F4/2, order 576 |
Convex | No |
Nature | Tame |
The retroantiprismatosnub disicositetrachoron, or rappisdi, is a nonconvex uniform polychoron that consists of 96 regular octahedra, 24 icosahedra, and 24 great icosahedra. 6 octahedra, 3 icosahedra, and 3 great icosahedra join at each vertex.
This polychoron has the same symmetry as the snub disicositetrachoron, with the octahedra acting as triangular antifrusta. It can be thought as a partial faceting of the small stellated hecatonicosachoron.
Cross-sections[edit | edit source]
Vertex coordinates[edit | edit source]
The vertices of a retroantiprismatosnub disicositetrachoron of edge length 1, centered at the origin, are given by all even permutations of:
Related polychora[edit | edit source]
The retroantiprismatosnub disicositetrachoron shares its vertices and edges with the small retrohemiantiprismatosnub prismatodisicositetrachoron and great retrohemiantiprismatosnub prismatodisicositetrachoron.
External links[edit | edit source]
- Bowers, Jonathan. "Category 20: Miscellaneous" (#971).
- Klitzing, Richard. "rappisdi".