vertex figure of pd{3,5,3}
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(at margins)
- between {3} and {(t,t,T,T)}: arccos(-sqrt[(5+2 sqrt(5))/15]) = 142.622632°
- between {(t,t,T,T)} and {(t,t,T,T)}: arccos(-1/sqrt(5)) = 116.565051°
| Acronym | teddoe |
| Name |
tetrahedrally diminished dodecahedron, vertex figure of pd{3,5,3} |
| |
| Circumradius | sqrt[(9+3 sqrt(5))/8] = 1.401259 |
| Vertex figure | [3,t,T,t], [T3] |
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Dihedral angles
(at margins) |
|
| Face vector | 16, 30, 16 |
| Confer | doe tet cube-dim-doe |
The non-regular (fxxx)-trapezia {(t,t,T,T)} are faceted regular pentagons. Its vertex angles are t = 72° resp. T = 108°. Their longer side is scaled by the golden ratio f = (1+sqrt(5))/2 = 1.618034. The triangles are regular, but use the f-scaled edges only.
This polyhedron is chiral and automorph.
12 * | 2 1 1 | 3 1 [3,t,T,t]
* 4 | 0 0 3 | 3 0 [T3]
-----+---------+-----
2 0 | 12 * * | 1 1 f-edges
2 0 | * 6 * | 2 0
1 1 | * * 12 | 2 0
-----+---------+-----
3 1 | 1 1 2 | 12 * (fxxx)-trapezium
3 0 | 3 0 0 | * 4 f-{3}
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