Acronym  ... 
Name  2quitgissid (?) 
Circumradius  sqrt[(3715 sqrt(5))/8] = 0.657550 
Vertex figure  2[6/2,10/3,10/3] 
General of army  f3o5x 
Colonel of regiment  quit gissid 
Confer 

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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