Acronym ...
Name 3gissid (?)
Circumradius (sqrt(5)-1) sqrt(3)/4 = 0.535233
Vertex figure 3[5/2,10/4,10/4]
General of army doe
Colonel of regiment gissid
Confer
non-Grünbaumian master:
gissid  
Grünbaumian relatives:
2gissid   6gissid  

Looks like a compound of 3 great stellated dodecahedra (gissid), and indeed vertices and edges both coincide by three, {5/2} and {10/4} coincide.


Incidence matrix according to Dynkin symbol

x5/4x5/2o

.   .   . | 60 |  1  2 |  2  1
----------+----+-------+------
x   .   . |  2 | 30  * |  2  0
.   x   . |  2 |  * 60 |  1  1
----------+----+-------+------
x5/4x   . | 10 |  5  5 | 12  *
.   x5/2o |  5 |  0  5 |  * 12

x5/4x5/3o

.   .   . | 60 |  1  2 |  2  1
----------+----+-------+------
x   .   . |  2 | 30  * |  2  0
.   x   . |  2 |  * 60 |  1  1
----------+----+-------+------
x5/4x   . | 10 |  5  5 | 12  *
.   x5/3o |  5 |  0  5 |  * 12

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