bi-tetrahedrally-diminished dodecahedron
(at margins)
- between {3} and {(t,T,T)}: arccos(-sqrt[(5+2 sqrt(5))/15]) = 142.622632°
- between {(t,T,T)} and {(t,T,T)}: arccos(-1/sqrt(5)) = 116.565051°
| Acronym | ... |
| Name |
cubically-diminished dodecahedron, bi-tetrahedrally-diminished dodecahedron |
| |
| Circumradius | sqrt[(9+3 sqrt(5))/8] = 1.401259 |
| Vertex figure | [3,t,3,T,T] |
|
Dihedral angles
(at margins) |
|
| Face vector | 12, 30, 20 |
| Confer | cube doe tet tet-dim-doe general pyritohedral ike |
The non-regular (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 f-scaled edges only.
This polyhedron can be seen as a special pyritohedral symmetric variant of ike. The according more general variant is oca cao aoc&#zd, then with d = sqrt[(a2-ac+c2)/2].
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 x-edges
oo. oo. oo.&#f & | 2 | * 24 | 1 1 f-edges
-----------------+----+------+-----
ox. ... ...&#f & | 3 | 1 2 | 12 * {(t,T,T)}
ooo ooo ooo&#f | 3 | 0 3 | * 8 {3}
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