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° Externallinks

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. 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
```