Acronym  sidditdid 
TOCID symbol  dID* 
Name 
small ditrigonary dodekicosidodecahedron, small dodekified icosidodecahedron 
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Circumradius  sqrt[(17+3 sqrt(5))/8] = 1.721489 
Vertex figure  [5/3,10,3,10] 
General of army  f3o5x 
Colonel of regiment  siid 
Dihedral angles 

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As abstract polytope sidditdid seems to be isomorphic to gidditdid, saddid, and gaddid, thereby replacing retrograde pentagrams and decagons respectively by pentagons and decagrams, by retrograde pentagons and decagons, by pentagrams and decagrams. At least all of those share the same incidence matrices. But in fact it is only isomorphic to gidditdid. This is because one hasn't only to consider the actual faces, but also the pseudo faces (holes) as well. Saddid and gaddid have square pseudo faces, while sidditdid and gidditdid have hexagonal holes instead.
As such sidditdid is a lieutenant.
This polyhedron is an edgefaceting of the small icosicosidodecahedron (siid).
Incidence matrix according to Dynkin symbol
x5/3o3x5*a . . .  60  2 2  1 2 1 +++ x . .  2  60 *  1 1 0 . . x  2  * 60  0 1 1 +++ x5/3o .  5  5 0  12 * * x . x5*a  10  5 5  * 12 * . o3x  3  0 3  * * 20
x3/2o5/2x5*a . . .  60  2 2  1 2 1 +++ x . .  2  60 *  1 1 0 . . x  2  * 60  0 1 1 +++ x3/2o .  3  3 0  20 * * x . x5*a  10  5 5  * 12 * . o5/2x  5  0 5  * * 12
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