Acronym ...
Name 3doe (?)
Circumradius sqrt[(9+3 sqrt(5))/8] = 1.401259
Vertex figure 3[5,10/2,10/2]
General of army doe
Colonel of regiment doe
Confer
non-Grünbaumian master:
doe  
Grünbaumian relatives:
2doe   6doe  

Looks like a compound of 3 dodecahedra (doe), and indeed vertices and edges both coincide by three, {5} and {10/2} coincide as well.


Incidence matrix according to Dynkin symbol

x5/2x5o

.   . . | 60 |  1  2 |  2  1
--------+----+-------+------
x   . . |  2 | 30  * |  2  0
.   x . |  2 |  * 60 |  1  1
--------+----+-------+------
x5/2x . | 10 |  5  5 | 12  *
.   x5o |  5 |  0  5 |  * 12

snubbed forms: β5/2x5o, x5/2β5o, β5/2β5o

o5/4x5/2x

.   .   . | 60 |  2  1 |  1  2
----------+----+-------+------
.   x   . |  2 | 60  * |  1  1
.   .   x |  2 |  * 30 |  0  2
----------+----+-------+------
o5/4x   . |  5 |  5  0 | 12  *
.   x5/2x | 10 |  5  5 |  * 12

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