Acronym ...
Name 2ike+4gad (?)
Circumradius sqrt[(5+sqrt(5))/8] = 0.951057
Vertex figure 10[6/2,10/2,10/2]
General of army ike
Colonel of regiment ike
Confer
non-Grünbaumian master:
gad   ike  
Grünbaumian relatives:
cid   ike+2gad   2ike+gad   ike+3gad   3ike+gad   3ike+3gad   4ike+gad   4ike+2gad   5ike+gad  

Looks like a compound of 2 icosahedra (ike) plus 4 great dodecahedra (gad), and indeed vertices coincide by ten, edges coincide by six, {10/2} coincide by pairs.


Incidence matrix according to Dynkin symbol

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

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