Acronym  ... 
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], [T^{3}] 
Dihedral angles
(at margins) 

Confer  doe tet cubedimdoe 
The nonregular (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 fscaled edges only.
This polyhedron is chiral and automorph.
12 *  2 1 1  3 1 [3,t,T,t] * 4  0 0 3  3 0 [T^{3}] ++ 2 0  12 * *  1 1 fedges 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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