Acronym ...
Name gird+12{10/4} (?)
Circumradius sqrt[-sqrt(5)+11/4] = 0.716891
Vertex figure 2[10/4,10/3,4]
General of army f3x5o
Colonel of regiment gaddid

Looks like a compound of a great rhombidodecahedron (gird) plus 12 {10/4} fitting into the dodecahedral set of holes, and indeed vertices and {10/4}-edges both coincide by pairs.


Incidence matrix according to Dynkin symbol

x5/4x5/3x

.   .   . | 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
----------+-----+----------+---------
x5/4x   . |  10 |  5  5  0 | 12  *  *
x   .   x |   4 |  2  0  2 |  * 30  *
.   x5/3x |  10 |  0  5  5 |  *  * 12

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