Acronym ...
Name giddy+20{6/2}
Circumradius sqrt[(17-3 sqrt(5))/8] = 1.134229
Vertex figure 2[6/2,10/3,6]
General of army tid
Colonel of regiment gidditdid

Looks like a compound of a great dodekicosahedron (giddy) plus 20 {6/2} fitting into the icosahedral set of holes, and indeed vertices and {6/2}-edges both coincide by pairs.


Incidence matrix according to Dynkin symbol

x3/2x5/3x3*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   .   x3*a |   6 |  3  0  3 |  * 20  *
.   x5/3x    |  10 |  0  5  5 |  *  * 12

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