Paragyrate diminished rhombicosidodecahedron |
---|
|
Rank | 3 |
---|
Type | CRF |
---|
Notation |
---|
Bowers style acronym | Pagydrid |
---|
Elements |
---|
Faces | 5+5+5 triangles, 5+5+5+10 squares, 1+5+5 pentagons, 1 decagon |
---|
Edges | 5+5+5+5+5+5+5+10+10+10+10+10+10+10 |
---|
Vertices | 5+5+5+10+10+10+10 |
---|
Vertex figures | 5+30 isosceles trapezoids, edge length 1, √2, (1+√5)/2, √2 |
---|
| 10 scalene triangles, edge lengths √2, (1+√5)/2, √(5+√5)/2 |
---|
| 10 irregular tetragons, edge lengths 1, √2, √2, (1+√5)/2 |
---|
Measures (edge length 1) |
---|
Circumradius | |
---|
Volume | |
---|
Dihedral angles | 3–4: |
---|
| 3–5: |
---|
| 4–4: |
---|
| 4–5: |
---|
| 4–10: |
---|
| 5–10: |
---|
Central density | 1 |
---|
Number of external pieces | 52 |
---|
Level of complexity | 42 |
---|
Related polytopes |
---|
Army | Pagydrid |
---|
Regiment | Pagydrid |
---|
Dual | Paradeltogyrate stellated deltoidal hexecontahedron |
---|
Conjugate | Paragyrate replenished quasirhombicosidodecahedron |
---|
Abstract & topological properties |
---|
Flag count | 420 |
---|
Euler characteristic | 2 |
---|
Surface | Sphere |
---|
Orientable | Yes |
---|
Genus | 0 |
---|
Properties |
---|
Symmetry | H2×I, order 10 |
---|
Convex | Yes |
---|
Nature | Tame |
---|
The paragyrate diminished rhombicosidodecahedron is one of the 92 Johnson solids (J77). It consists of 5+5+5 triangles, 5+5+5+10 squares, 1+5+5 pentagons, and 1 decagon. It can be constructed by removing one of the pentagonal cupolaic caps of the small rhombicosidodecahedron, and rotating the opposite cap by 36°.
A paragyrate diminished rhombicosidodecahedron of edge length 1 has vertices given by:
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- .