Acronym	sidditdid
TOCID symbol	dID*
Name	small ditrigonary dodekicosidodecahedron, small dodekified icosidodecahedron
	© ©
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	between {3} and {10}:   arccos(-sqrt[(5-2 sqrt(5))/15]) = 100.812317° between {5/2} and {10}:   arccos(1/sqrt(5)) = 63.434949°
Face vector	60, 120, 44
Confer	general polytopal classes: Wythoffian polyhedra
External links

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 edge-faceting 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