Acronym  ... 
Name 
cubicallydiminished dodecahedron, bitetrahedrallydiminished dodecahedron 
 
Circumradius  sqrt[(9+3 sqrt(5))/8] = 1.401259 
Vertex figure  [3,t,3,T,T] 
Dihedral angles
(at margins) 

Confer  cube doe tet tetdimdoe 
The nonregular (ffx)triangles {(t,T,T)} are faceted regular pentagons. Its vertex angles are t = 36° resp. T = 72°. Their longer side tT is scaled by the golden ratio f = (1+sqrt(5))/2 = 1.618034. The regular triangles use the fscaled edges only.
This polyhedron can be seen as a pyritohedral symmetric variant of ike.
Incidence matrix according to Dynkin symbol
oxF xFo Fox&#zf (F=ff) → heights = 0 (tegum sum of 3 mutually perp. (x,F){4}) o.. o.. o.. &  12  1 4  3 2 +++ ... x.. ... &  2  6 *  2 0 xedges oo. oo. oo.&#f &  2  * 24  1 1 fedges +++ ox. ... ...&#f &  3  1 2  12 * {(t,T,T)} ooo ooo ooo&#f  3  0 3  * 8 {3}
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