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

Looks like a compound of 2 great dodecahedra (gad) plus an icosahedron (ike), and indeed vertices coincide by five, edges coincide by three.


Incidence matrix according to Dynkin symbol

x5/2x3o

.   . . | 60 |  1  2 |  2  1
--------+----+-------+------
x   . . |  2 | 30  * |  2  0
.   x . |  2 |  * 60 |  1  1
--------+----+-------+------
x5/2x . | 10 |  5  5 | 12  *
.   x3o |  3 |  0  3 |  * 20

o3/2x5/2x

.   .   . | 60 |  2  1 |  1  2
----------+----+-------+------
.   x   . |  2 | 60  * |  1  1
.   .   x |  2 |  * 30 |  0  2
----------+----+-------+------
o3/2x   . |  3 |  3  0 | 20  *
.   x5/2x | 10 |  5  5 |  * 12

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