Acronym ...
Name sidtid+ditdid+gidtid (?)
Circumradius sqrt(3)/2 = 0.866025
Vertex figure 6[6/2,4,10/2]/0
General of army doe
Colonel of regiment sidtid
Confer sidtid+ditdid   sidtid+gidtid   ditdid+gidtid   sicdatrid   cadditradid   gicdatrid   2sidtid+5cube   2ditdid+5cube   2gidtid+5cube   3sidtid   3gidtid  

Looks like a compound of a small ditrigonal icosidodecahedron (sidtid) plus a ditrigonal dodecadodecahedron (ditdid) plus a great ditrigonal icosidodecahedron (gidtid), and indeed vertices coincide by 6, edges coincide by three.


Incidence matrix according to Dynkin symbol

x3/2x5/2x

.   .   . | 120 |  1  1  1 |  1  1  1
----------+-----+----------+---------
x   .   . |   2 | 60  *  * |  1  1  0
.   x   . |   2 |  * 60  * |  1  0  1
.   .   x |   2 |  *  * 60 |  0  1  1
----------+-----+----------+---------
x3/2x   . |   6 |  3  3  0 | 20  *  *
x   .   x |   4 |  2  0  2 |  * 30  *
.   x5/2x |  10 |  0  5  5 |  *  * 12

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