Acronym  ... 
Name  3doe (?) 
Circumradius  sqrt[(9+3 sqrt(5))/8] = 1.401259 
Vertex figure  3[5,10/2,10/2] 
General of army  doe 
Colonel of regiment  doe 
Confer 

Looks like a compound of 3 dodecahedra (doe), and indeed vertices and edges both coincide by three, {5} and {10/2} coincide as well.
Incidence matrix according to Dynkin symbol
x5/2x5o . . .  60  1 2  2 1 +++ x . .  2  30 *  2 0 . x .  2  * 60  1 1 +++ x5/2x .  10  5 5  12 * . x5o  5  0 5  * 12 snubbed forms: β5/2x5o, x5/2β5o, β5/2β5o
o5/4x5/2x . . .  60  2 1  1 2 +++ . x .  2  60 *  1 1 . . x  2  * 30  0 2 +++ o5/4x .  5  5 0  12 * . x5/2x  10  5 5  * 12
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