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°
Face vector	60, 120, 44
Confer	general polytopal classes: Wythoffian polyhedra
External links

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. At least all of those share the same incidence matrices. 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