Acronym ...
Name 2quitgissid (?)
Circumradius sqrt[(37-15 sqrt(5))/8] = 0.657550
Vertex figure 2[6/2,10/3,10/3]
General of army f3o5x
Colonel of regiment quit gissid
Confer
non-Grünbaumian master:
quit gissid  

Looks like a compound of 2 quasitruncated great stellated dodecahedra (quit gissid), and indeed vertices, edges, and {10/3} all coincide by pairs.


Incidence matrix according to Dynkin symbol

x3/2x5/3x5/3*a

.   .   .      | 120 |  1  1  1 |  1  1  1
---------------+-----+----------+---------
x   .   .      |   2 | 60  *  * |  1  1  0
.   x   .      |   2 |  * 60  * |  1  0  1
.   .   x      |   2 |  *  * 60 |  0  1  1
---------------+-----+----------+---------
x3/2x   .      |   6 |  3  3  0 | 20  *  *
x   .   x5/3*a |  10 |  5  0  5 |  * 12  *
.   x5/3x      |  10 |  0  5  5 |  *  * 12

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