Pentagonal-icosidodecahedral duoprism
Jump to navigation
Jump to search
Pentagonal-icosidodecahedral duoprism | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Pid |
Coxeter diagram | x5o o5x3o () |
Elements | |
Tera | 20 triangular-pentagonal duoprisms, 12 pentagonal duoprisms, 5 icosidodecahedral prisms |
Cells | 100 triangular prisms, 60+60 pentagonal prisms, 5 icosidodecahedra |
Faces | 100 triangles, 300 squares, 30+60 pentagons |
Edges | 150+300 |
Vertices | 150 |
Vertex figure | Rectangular scalene, edge lengths 1, (1+√5)/2, 1, (1+√5)/2 (base rectangle), (1+√5)/2 (top), √2 (side edges) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Trapedip–pip–pedip: |
Iddip–id–iddip: 108° | |
Trapedip–trip–iddip: 90° | |
Pedip–pip–iddip: 90° | |
Central density | 1 |
Number of external pieces | 37 |
Level of complexity | 20 |
Related polytopes | |
Army | Pid |
Regiment | Pid |
Dual | Pentagonal-rhombic triacontahedral duotegum |
Conjugate | Pentagrammic-great icosidodecahedral duoprism |
Abstract & topological properties | |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | H3×H2, order 1200 |
Convex | Yes |
Nature | Tame |
The pentagonal-icosidodecahedral duoprism or pid is a convex uniform duoprism that consists of 5 icosidodecahedral prisms, 12 pentagonal duoprisms, and 20 triangular-pentagonal duoprisms. Each vertex joins 2 icosidodecahedral prisms, 2 triangular-pentagonal duoprisms, and 2 pentagonal duoprisms.
Vertex coordinates[edit | edit source]
The vertices of a pentagonal-icosidodecahedral duoprism of edge length 1 are given by all permutations of the last three coordinates of:
as well as all even permutations of the last three coordinates of:
External links[edit | edit source]
- Klitzing, Richard. "pid".