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° Externallinks

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. 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
```