Great icosicosidodecahedron

Great icosicosidodecahedron
(3D model) (OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Giid
Coxeter diagram	o3/2x3x5*a ()
Elements
Faces	20 triangles, 12 pentagons, 20 hexagons
Edges	60+60
Vertices	60
Vertex figure	Crossed isosceles trapezoid, edge lengths 1, √3, (1+√5)/2, √3
Measures (edge length 1)
Circumradius	$\sqrt{\frac{17-3\sqrt5}{8}} \approx 1.13423$
Volume	$\frac{29\sqrt5-30}{3} \approx 11.61533$
Dihedral angles	5–6: $\arccos\left(\sqrt{\frac{5-2\sqrt5}{15}}\right) \approx 79.18768^\circ$
	3–6: $\arccos\left(\frac{\sqrt5}{3}\right) \approx 41.81032^\circ$
Central density	6
Number of external pieces	1232
Level of complexity	75
Related polytopes
Army	Tid, edge length $\frac{3-\sqrt5}{2}$
Regiment	Gidditdid
Dual	Great icosacronic hexecontahedron
Conjugate	Small icosicosidodecahedron
Convex core	Icosahedron
Abstract & topological properties
Flag count	480
Euler characteristic	–8
Orientable	Yes
Genus	5
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

The great icosicosidodecahedron, or giid, is a uniform polyhedron. It consists of 20 triangles, 12 pentagons, and 20 hexagons. One triangle, one pentagon, and two hexagons join at each vertex.

It is a faceting of the great ditrigonal dodecicosidodecahedron, using its 12 pentagons and 20 triangles along with 20 additional hexagons.

A semi-uniform variant of this polyhedron can be constructed as a rectified great ditrigonary icosidodecahedron.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the great ditrigonal dodecicosidodecahedron.

Related polyhedra

o3/2o3o5*a truncations

Name	OBSA	CD diagram	Picture
Great ditrigonary icosidodecahedron	gidtid	x3/2o3o5*a ()
(degenerate, 3ike+gad)		x3/2x3o5*a ()
(degenerate, double cover of gike)		o3/2x3o5*a ()
Great icosicosidodecahedron	giid	o3/2x3x5*a ()
Great ditrigonary icosidodecahedron	gidtid	o3/2o3x5*a ()
(degenerate, double cover of seihid)		x3/2o3x5*a ()
(degenerate, siddy+20(6/2))		x3/2x3x5*a ()
(degenerate, 5ike+gad)		s3/2s3s5*a

External links

• Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#49).

• Klitzing, Richard. "giid".

• Wikipedia Contributors. "Great icosicosidodecahedron".
• McCooey, David. "Great Icosicosidodecahedron"