Acronym	gaddid
TOCID symbol	eJE*
Name	great dodekicosidodecahedron
	© ©
Circumradius	sqrt[-sqrt(5)+11/4] = 0.716891
Vertex figure	[5/2,10/3,3,10/3]
General of army	f3x5o
Colonel of regiment	(is itself locally convex – other uniform polyhedral members: qrid   gird – other edge facetings)
Dihedral angles	between {5/2} and {10/3}:   arccos(-1/sqrt(5)) = 116.565051° between {3} and {10/3}:   arccos(-sqrt[(5-2 sqrt(5))/15]) = 100.812317°
Face vector	60, 120, 44
Confer	general polytopal classes: Wythoffian polyhedra
External links

As abstract polytope gaddid seems to be isomorphic to saddid, sidditdid, and gidditdid, thereby replacing pentagrams and decagrams respectively by retrograde pentagons and decagons, 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 saddid. 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.

Incidence matrix according to Dynkin symbol

x5/3x5/2o3*a

.   .   .    | 60 |  2  2 |  2  1  1
-------------+----+-------+---------
x   .   .    |  2 | 60  * |  1  1  0
.   x   .    |  2 |  * 60 |  1  0  1
-------------+----+-------+---------
x5/3x   .    | 10 |  5  5 | 12  *  *
x   .   o3*a |  3 |  3  0 |  * 20  *
.   x5/2o    |  5 |  0  5 |  *  * 12

x3/2o5/3x5/3*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   .   x5/3*a | 10 |  5  5 |  * 12  *
.   o5/3x      |  5 |  0  5 |  *  * 12