Great ditrigonal dodecicosidodecahedron

Great ditrigonal dodecicosidodecahedron
(3D model) (OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gidditdid
Coxeter diagram	x5/3x3o5*a ()
Elements
Faces	20 triangles, 12 pentagons, 12 decagrams
Edges	60+60
Vertices	60
Vertex figure	Isosceles trapezoid, edge lengths 1, √(5–√5)/2, (1+√5)/2, √(5–√5)/2
Measures (edge length 1)
Circumradius	$\sqrt{\frac{17-3\sqrt5}{8}} ≈ 1.13423$
Volume	$7\frac{15-\sqrt5}{6} ≈ 14.89125$
Dihedral angles	3–10/3: $\arccos\left(-\sqrt{\frac{5+2\sqrt5}{15}}\right) ≈ 142.62263°$
	5–10/3: $\arccos\left(-\frac{\sqrt5}{5}\right) ≈ 116.56505°$
Central density	4
Number of external pieces	152
Level of complexity	13
Related polytopes
Army	Tid, edge length $\frac{3-\sqrt5}{2}$
Regiment	Gidditdid
Dual	Great ditrigonal dodecacronic hexecontahedron
Conjugate	Small ditrigonal dodecicosidodecahedron
Convex core	Dodecahedron
Abstract & topological properties
Flag count	480
Euler characteristic	-16
Orientable	Yes
Genus	9
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

The great ditrigonal dodecicosidodecahedron, or gidditdid, is a uniform polyhedron. It consists of 20 triangles, 12 pentagons, and 12 decagrams. One triangle, one pentagon, and two decagrams join at each vertex.

Vertex coordinates

A great ditrigonal dodecicosidodecahedron of edge length 1 has vertex coordinates given by all even permutations of:

• $\left(±\frac12,\,±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{4}\right),$
• $\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5}{2}\right),$
• $\left(±\frac12,\,±1,\,±\frac{3-\sqrt5}{4}\right).$

Related polyhedra

The great ditrigonal dodecicosidodecahedron is the colonel of a three-member regiment that also includes the great icosicosidodecahedron and the great dodecicosahedron.

External links

• Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#48).

• Klitzing, Richard. "gidditdid".

• Wikipedia Contributors. "Great ditrigonal dodecicosidodecahedron".
• McCooey, David. "Great ditrigonal Dodecicosidodecahedron"