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

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


Incidence matrix according to Dynkin symbol

x3/2x5/2o5*a

.   .   .    | 60 |  2  2 |  2  1  1
-------------+----+-------+---------
x   .   .    |  2 | 60  * |  1  1  0
.   x   .    |  2 |  * 60 |  1  0  1
-------------+----+-------+---------
x3/2x   .    |  6 |  3  3 | 20  *  *
x   .   o5*a |  5 |  5  0 |  * 12  *
.   x5/2o    |  5 |  0  5 |  *  * 12

o5/4x3/2x5/3*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  *  *
.   x3/2x      |  6 |  3  3 |  * 20  *
o    .  x5/3*a |  5 |  0  5 |  *  * 12

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