Acronym	gad
TOCID symbol	E
Name	great dodecahedron, faceted icosahedron, vertex figure of fix
	© ©   ©
Circumradius	sqrt[(5+sqrt(5))/8] = 0.951057
Inradius	sqrt[(5+sqrt(5))/40] = 0.425325
Density	3
Vertex figure	[55]/2
Vertex layers	Layer Symmetry Subsymmetries   o5o5/2o o5o   . o .   o . o5/2o 1 x5o5/2o o5o   . x .   o edge first . o5/2o vertex first 2 x5o   . {5} first o .   f . f5/2o vertex figure 3 o5x   . opposite {5} f .   x . o5/2f 4 o5o   . o .   f . o5/2o opposite vertex 5   x .   o opposite edge
Lace city in approx. ASCII-art	o o f x x f o o
Coordinates	(τ/2, 1/2, 0)   & even permutations, all changes of sign where τ = (1+sqrt(5))/2
General of army	ike
Colonel of regiment	ike
Dual	sissid
Dihedral angles	between {5} and {5}:   arccos(1/sqrt(5)) = 63.434949°
Face vector	12, 30, 12
Confer	Grünbaumian relatives: 2gad   cid   ike+2gad   2ike+gad   ike+3gad   3ike+gad   3ike+3gad   4ike+gad   5ike+gad   2ike+4gad   4ike+2gad   compounds: presipsido   presipsi   general polytopal classes: Wythoffian polyhedra   regular   noble polytopes
External links

As abstract polytope gad is isomorphic to sissid, thereby replacing facial pentagons by pentagrams and conversely vertex figure pentagrams by corresponding pentagons. – As such gad is a lieutenant. Both gad and sissid can be seen as different realizations of the same self-dual regular abstract polyhedron {5,5}₆ (where the index just denotes the size of the corresponding Petrie polygon).

This polyhedron is an edge-faceting of the icosahedron (ike).

Incidence matrix according to Dynkin symbol

o5/2o5x

.   . . | 12 |  5 |  5
--------+----+----+---
.   . x |  2 | 30 |  2
--------+----+----+---
.   o5x |  5 |  5 | 12

snubbed forms: o5/2o5β

o5/3o5x

.   . . | 12 |  5 |  5
--------+----+----+---
.   . x |  2 | 30 |  2
--------+----+----+---
.   o5x |  5 |  5 | 12

x5/4o5/2o

.   .   . | 12 |  5 |  5
----------+----+----+---
x   .   . |  2 | 30 |  2
----------+----+----+---
x5/4o   . |  5 |  5 | 12

x5/4o5/3o

.   .   . | 12 |  5 |  5
----------+----+----+---
x   .   . |  2 | 30 |  2
----------+----+----+---
x5/4o   . |  5 |  5 | 12