Triacontaditeric pentacomb
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| Triacontaditeric pentacomb | |
|---|---|
| Rank | 6 |
| Type | Regular, paracompact |
| Space | Hyperbolic |
| Notation | |
| Coxeter diagram | x3o3o3o4o3o (    ) |
| Schläfli symbol | {3,3,3,4,3} |
| Elements | |
| Peta | 3MN triacontaditera |
| Tera | 48MN pentachora |
| Cells | 80MN tetrahedra |
| Faces | 40MN triangles |
| Edges | 5MN |
| Vertices | 10N |
| Vertex figure | Hexadecachoric tetracomb, edge length 1 |
| Measures (edge length 1) | |
| Circumradius | |
| Related polytopes | |
| Army | Triacontaditeric pentacomb |
| Regiment | Triacontaditeric pentacomb |
| Dual | Icositetrachoric tetracomb pentacomb |
| Abstract & topological properties | |
| Orientable | Yes |
| Properties | |
| Symmetry | [3,4,3,3,3] |
| Convex | Yes |
The triacontaditeric pentacomb is a paracompact regular tiling of 5D hyperbolic space. It is paracompact because it has infinite Euclidean vertex figures, with all vertices as ideal points. 3 triacontaditera meet at each cell, and infinitely many meet at each vertex, forming a hexadecachoric tetracomb as the vertex figure.
Representations[edit | edit source]
A triacontaditeric pentacomb has the following Coxeter diagrams:
- x3o3o3o4o3o () (full symmetry)
- x3o3o3o4o *c3o (
) (demitesseractic tetracomb verf) - x3o3o3o *c3o *c3o (
) (quartertesseractic tetracomb verf)
External links[edit | edit source]
- Klitzing, Richard. "x3o3o3o4o3o".
- Wikipedia contributors. "5-orthoplex honeycomb".