Pentagonal cupofastegium
Jump to navigation
Jump to search
Pentagonal cupofastegium | |
---|---|
Rank | 4 |
Type | Segmentotope |
Notation | |
Bowers style acronym | Pecuf |
Coxeter diagram | ox xx5xo&#x |
Elements | |
Cells | 5 tetrahedra, 5 triangular prisms, 1 pentagonal prism, 2 pentagonal cupolas |
Faces | 10+10 triangles, 5+10 squares, 2 pentagons, 1 decagon |
Edges | 5+5+5+10+20 |
Vertices | 10+10 |
Vertex figures | 10 isosceles trapezoidal pyramids, base edge lengths 1, √2, (1+√5)/2, √2, side edge lengths 1, 1, √2. √2 |
10 sphenoids, edge lengths 1 (3), √2 (2), and √(5+√5)/2 (1) | |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dichoral angles | Tet–3–trip: |
Pip–4–trip: | |
Pecu–10–pecu: 144° | |
Pecu–3–tet: | |
Pecu–4–trip: | |
Pip–5–pecu: 18° | |
Heights | Peg atop pecu: |
Pip atop dec: | |
Central density | 1 |
Related polytopes | |
Army | Pecuf |
Regiment | Pecuf |
Dual | Pentagonal cupolanotch |
Conjugate | Retrograde pentagrammic cupofastegium |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | H2×A1×I, order 20 |
Convex | Yes |
Nature | Tame |
The pentagonal cupofastegium, or pecuf, also sometimes called the pentagonal orthobicupolic ring, is a CRF segmentochoron (designated K-4.154 on Richard Klitzing's list). It consists of 1 pentagonal prism, 5 tetrahedra, 5 triangular prisms, and 2 pentagonal cupolas.
It has two representations as a segmentochoron: pentagon atop pentagonal cupola or pentagonal prism atop decagon.
The pentagonal cupofastegium can be obtained as a cap of the small disprismatohexacosihecatonicosachoron in pentagonal prism first orientation.
Vertex coordinates[edit | edit source]
The vertices of a pentagonal cupofastegium with edge length 1 are given by:
Representations[edit | edit source]
A pentagonal cupofastegium has the following Coxeter diagrams:
- ox xx5xo&#x (full symmetry)
- xxx5oxo&#x (H2 symmetry only, seen with pentagon atop pentagonal cupola)
External links[edit | edit source]
- Klitzing, Richard. "pecuf".