Pentagonal antitegum
Pentagonal antitegum | |
---|---|
Rank | 3 |
Type | Uniform dual |
Notation | |
Bowers style acronym | Pat |
Coxeter diagram | p2p10o () |
Conway notation | dA5 |
Elements | |
Faces | 10 kites |
Edges | 10+10 |
Vertices | 2+10 |
Vertex figure | 2 pentagons, 10 triangles |
Measures (edge lengths 1, ) | |
Dihedral angle | |
Central density | 1 |
Number of external pieces | 10 |
Level of complexity | 4 |
Related polytopes | |
Army | Pat |
Regiment | Pat |
Dual | Pentagonal antiprism |
Conjugate | Pentagrammic retroantitegum |
Abstract & topological properties | |
Flag count | 80 |
Euler characteristic | 2 |
Surface | Sphere |
Orientable | Yes |
Genus | 0 |
Properties | |
Symmetry | (I2(10)×A1)/2, order 20 |
Convex | Yes |
Nature | Tame |
The pentagonal antitegum, also known as the pentagonal trapezohedron, is an antitegum based on the pentagon, constructed as the dual of a pentagonal antiprism. It has 10 kites as faces, with 2 order–5 and 10 order–3 vertices.
Each face of this polyhedron is a kite with its longer edges times the length of its shorter edges. These kites have 3 angles measuring 108° and 1 measuring 36°.
The pentagonal antitegum can be constructed from the regular dodecahedron by augmenting tall pyramids on two opposite faces.
In tabletop games, it is a popular design for a 10-sided die or "d10." A standard set of dice used in role-playing games comprises the five Platonic solids and two d10s, one marked with the numbers 0-9 and the other with the multiples of 10 from 00-90.
External links[edit | edit source]
- Klitzing, Richard. "p2p5p".
- Wikipedia contributors. "Pentagonal trapezohedron".
- McCooey, David. "Pentagonal Trapezohedron"