Acronym saddid TOCID symbol dID Name small dodekicosidodecahedron ` © ©` Circumradius sqrt[sqrt(5)+11/4] = 2.232951 Vertex figure [3/2,10,5,10] Snub derivation General of army srid Colonel of regiment srid Dihedral angles between {5} and {10}:   arccos(-1/sqrt(5)) = 116.565051° between {3} and {10}:   arccos(sqrt[(5+2 sqrt(5))/15]) = 37.377368° Externallinks

As abstract polytope saddid seems to be isomorphic to gaddid, sidditdid, and gidditdid, thereby replacing retrograde pentagons and decagons respectively by pentagrams and decagrams, by retrograde pentagrams and decagons, by pentagons and decagrams. But in fact it is only isomorphic to gaddid. 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 saddid is a lieutenant.

This polyhedron is an edge-faceting of the small rhombicosidodecahedron (srid).

Incidence matrix according to Dynkin symbol

```x3/2o5x5*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  *
.   o5x    |  5 |  0  5 |  *  * 12
```

```x5/4o3x5*a

.   . .    | 60 |  2  2 |  1  2  1
-----------+----+-------+---------
x   . .    |  2 | 60  * |  1  1  0
.   . x    |  2 |  * 60 |  0  1  1
-----------+----+-------+---------
x5/4o .    |  5 |  5  0 | 12  *  *
x   . x5*a | 10 |  5  5 |  * 12  *
.   o3x    |  3 |  0  3 |  *  * 20
```

```β3o5x

both( . . . ) | 60 |  2  2 |  1  1  2
--------------+----+-------+---------
both( . . x ) |  2 | 60  * |  0  1  1
sefa( β3o . ) |  2 |  * 60 |  1  0  1
--------------+----+-------+---------
β3o .   ♦  3 |  0  3 | 20  *  *
both( . o5x ) |  5 |  5  0 |  * 12  *
sefa( β3o5x ) | 10 |  5  5 |  *  * 12

starting figure: x3o5x
```