Great dodecicosahedron

Great dodecicosahedron
(3D model) (OFF file)
Rank	3
Type	Uniform
Notation
Bowers style acronym	Giddy
Elements
Faces	20 hexagons, 12 decagrams
Edges	60+60
Vertices	60
Vertex figure	Butterfly, edge lengths √3 and √(5–√5)/2
Measures (edge length 1)
Circumradius	${\sqrt {\frac {17-3{\sqrt {5}}}{8}}}\approx 1.13423$
Dihedral angles	6–10/3 #1: $\arccos \left(-{\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 100.81232^{\circ }$
	6–10/3 #2: $\arccos \left({\sqrt {\frac {5+2{\sqrt {5}}}{15}}}\right)\approx 37.37737^{\circ }$
Central density	even
Number of external pieces	912
Level of complexity	56
Related polytopes
Army	Tid, edge length ${\frac {3-{\sqrt {5}}}{2}}$
Regiment	Gidditdid
Dual	Great dodecicosacron
Conjugate	Small dodecicosahedron
Convex core	Icosahedron
Abstract & topological properties
Flag count	480
Euler characteristic	–28
Orientable	No
Genus	30
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

The great dodecicosahedron, or giddy, is a uniform polyhedron. It consists of 20 hexagons and 12 decagrams. Two hexagons and two decagrams meet at each vertex.

It is a faceting of the great ditrigonal dodecicosidodecahedron, using its 12 decagrams along with the 20 hexagons of the great icosicosidodecahedron.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#50).

• Klitzing, Richard. "giddy".
• Wikipedia contributors. "Great dodecicosahedron".
• McCooey, David. "Great Dodecicosahedron"