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

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


Incidence matrix according to Dynkin symbol

x5/4x3o5*a

.   . .    | 60 |  2  2 |  2  1  1
-----------+----+-------+---------
x   . .    |  2 | 60  * |  1  1  0
.   x .    |  2 |  * 60 |  1  0  1
-----------+----+-------+---------
x5/4x .    | 10 |  5  5 | 12  *  *
x   . o5*a |  5 |  5  0 |  * 12  *
.   x3o    |  3 |  0  3 |  *  * 20

x5/4x5/4o3/2*a

.   .   .      | 60 |  2  2 |  2  1  1
---------------+----+-------+---------
x   .   .      |  2 | 60  * |  1  1  0
.   x   .      |  2 |  * 60 |  1  0  1
---------------+----+-------+---------
x5/4x   .      | 10 |  5  5 | 12  *  *
x   .   o3/2*a |  3 |  3  0 |  * 20  *
.   x5/4o      |  5 |  0  5 |  *  * 12

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