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°
Face vector	60, 120, 52
Confer	general polytopal classes: Wythoffian polyhedra
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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