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

Looks like a compound of an icosahedron (ike) plus 3 great dodecahedra (gad), and indeed vertices coincide by five, edges coincide by four, {5} and {10/2} coincide.


Incidence matrix according to Dynkin symbol

o3/2x5/2x5*a

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

o5/4x5/2x3*a

.   .   .    | 60 |  2  2 |  1  2  1
-------------+----+-------+---------
.   x   .    |  2 | 60  * |  1  1  0
.   .   x    |  2 |  * 60 |  0  1  1
-------------+----+-------+---------
o5/4x   .    |  5 |  5  0 | 12  *  *
.   x5/2x    | 10 |  5  5 |  * 12  *
o   .   x3*a |  3 |  0  3 |  *  * 20

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