Acronym ...
Name 2gike (?)
Circumradius sqrt[(5-sqrt(5))/8] = 0.587785
Vertex figure [310]/4
General of army ike
Colonel of regiment sissid
Confer
non-Grünbaumian master:
gike  
Grünbaumian relatives:
2gike+sissid   4sissid+2gike  

Looks like a compound of 2 great icosahedra (gike), and indeed edges and faces both coincide by pairs, but vertices are identified.

As abstract polytope 2gike is isomorphic to 2ike.


Incidence matrix according to Dynkin symbol

o3/2x3o5*a

.   . . | 12 | 10 |  5  5
--------+----+----+------
.   x . |  2 | 60 |  1  1
--------+----+----+------
o3/2x . |  3 |  3 | 20  *
.   x3o |  3 |  3 |  * 20

o5/4o3x3*a

.   . .    | 12 | 10 |  5  5
-----------+----+----+------
.   . x    |  2 | 60 |  1  1
-----------+----+----+------
.   o3x    |  3 |  3 | 20  *
o   . x3*a |  3 |  3 |  * 20

o5/4o3/2x3/2*a

.   .   .      | 12 | 10 |  5  5
---------------+----+----+------
.   .   x      |  2 | 60 |  1  1
---------------+----+----+------
.   o3/2x      |  3 |  3 | 20  *
o   .   x3/2*a |  3 |  3 |  * 20

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