Acronym tepdid Name tripentadiminished icosidodecahedron Circumradius (1+sqrt(5))/2 = 1.618034 Vertex figures [3,Q,3,Q], [q,3,T,5], [5,t,5,t], [T,3,T,5] Confer uniform relative: id   related Johnson solids: teddi   faceting of: id

This polyhedron has 4 different types of faces: regular triangles of edge size x, acute triangles {(t,T,T)} of edge sequence xff (in fact ox&#f, i.e. with corner angles t = 36° resp. T = 72°), trapezia {(q,q,Q,Q)} of edge sequence xxxf (in fact xf&#x, i.e. with corner angles q = 72° resp: Q = 108°), and regular pentagons of edge size f.

Those large pentagons occur as "sefas" (sectioning facets) underneath 3 of the pentagons of id, and the acute triangles as well as the trapezia result as remainders of the other pentagons of id. In the above picture the outline of the non-diminished id is shown as guidance to the eye.

Incidence matrix according to Dynkin symbol

```xfFo3oxox&#(x,f)t   → height(1,2) = 1/sqrt(3) = 0.577350
height(2,3) = 2/sqrt(3) + sqrt([3-sqrt(5)]/6) = 1.511523
height(3,4) = 1/sqrt(3) + sqrt([3-sqrt(5)]/6) = 0.934172

o...3o...     | 3 * * * | 2 2 0 0 0 0 0 | 1 2 1 0 0 0 0  [3,Q,3,Q]
.o..3.o..     | * 6 * * | 0 1 1 1 1 0 0 | 0 1 1 1 1 0 0  [q,3,T,5]
..o.3..o.     | * * 3 * | 0 0 0 0 2 2 0 | 0 0 0 2 1 1 0  [5,t,5,t]
...o3...o     | * * * 3 | 0 0 0 0 0 2 2 | 0 0 0 1 0 2 1  [T,3,T,5]
--------------+---------+---------------+--------------
x... ....     | 2 0 0 0 | 3 * * * * * * | 1 1 0 0 0 0 0  x
oo..3oo..&#x  | 1 1 0 0 | * 6 * * * * * | 0 1 1 0 0 0 0  x
.f.. ....     | 0 2 0 0 | * * 3 * * * * | 0 1 0 1 0 0 0  f
.... .x..     | 0 2 0 0 | * * * 3 * * * | 0 0 1 0 1 0 0  x
.oo.3.oo.&#f  | 0 1 1 0 | * * * * 6 * * | 0 0 0 1 1 0 0  f
..oo3..oo&#f  | 0 0 1 1 | * * * * * 6 * | 0 0 0 1 0 1 0  f
.... ...x     | 0 0 0 2 | * * * * * * 3 | 0 0 0 0 0 1 1  x
--------------+---------+---------------+--------------
x...3o...     | 3 0 0 0 | 3 0 0 0 0 0 0 | 1 * * * * * *  x-{3}
xf.. ....&#x  | 2 2 0 0 | 1 2 1 0 0 0 0 | * 3 * * * * *  {(q,q,Q,Q)}
.... ox..&#x  | 1 2 0 0 | 0 2 0 1 0 0 0 | * * 3 * * * *  x-{3}
.fFo ....&#ft | 0 2 2 1 | 0 0 1 0 2 2 0 | * * * 3 * * *  f-{5}
.... .xo.&#f  | 0 2 1 0 | 0 0 0 1 2 0 0 | * * * * 3 * *  {(t,T,T)}
.... ..ox&#f  | 0 0 1 2 | 0 0 0 0 0 2 1 | * * * * * 3 *  {(t,T,T)}
...o3...x     | 0 0 0 3 | 0 0 0 0 0 0 3 | * * * * * * 1  x-{3}
```