Acronym giid TOCID symbol iJE Name great icosicosidodecahedron ` © ©` Circumradius sqrt[(17-3 sqrt(5))/8] = 1.134229 Vertex figure [3/2,6,5,6] General of army tid Colonel of regiment gidditdid Dihedral angles between {5} and {6}:   arccos(sqrt[(5-2 sqrt(5))/15]) = 79.187683° between {3} and {6}:   arccos(sqrt(5)/3) = 41.810315° Externallinks

As abstract polytope giid is isomorphic to siid, thereby replacing pentagons by pentagrams and retrograde triangles by prograde ones. – As such giid is a lieutenant.

This polyhedron is an edge-faceting of the great ditrigonary dodekicosidodecahedron (gidditdid).

Incidence matrix according to Dynkin symbol

```o3/2x3x5*a

.   . .    | 60 |  2  2 |  1  2  1
-----------+----+-------+---------
.   x .    |  2 | 60  * |  1  1  0
.   . x    |  2 |  * 60 |  0  1  1
-----------+----+-------+---------
o3/2x .    |  3 |  3  0 | 20  *  *
.   x3x    |  6 |  3  3 |  * 20  *
o   . x5*a |  5 |  0  5 |  *  * 12
```

```x5/4o3x3*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   . x3*a |  6 |  3  3 |  * 20  *
.   o3x    |  3 |  0  3 |  *  * 20
```