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}

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