Great ditrigonary icosidodecahedron

Great ditrigonary icosidodecahedron
(3D model) (OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gidtid
Coxeter diagram	x3/2o3o5*a ()
Elements
Faces	20 triangles, 12 pentagons
Edges	60
Vertices	20
Vertex figure	Tripod, edge lengths 1 and (1+√5)/2
Measures (edge length 1)
Circumradius	$\frac{\sqrt3}{2} ≈ 0.86603$
Volume	$\frac{4\sqrt5}{3} ≈ 2.98142$
Dihedral angle	$\arccos\left(\sqrt{\frac{5-2\sqrt5}{15}}\right) ≈ 79.18768^\circ$
Central density	6
Number of external pieces	300
Level of complexity	15
Related polytopes
Army	Doe, edge length $\frac{\sqrt5-1}{2}$
Regiment	Sidtid
Dual	Great triambic icosahedron
Conjugate	Small ditrigonary icosidodecahedron
Convex core	Dodecahedron
Abstract & topological properties
Flag count	240
Euler characteristic	–8
Orientable	Yes
Genus	5
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

The great ditrigonary icosidodecahedron or gidtid is a quasiregular uniform polyhedron. It consists of 20 equilateral triangles and 12 pentagons, with three of each joining at a vertex.

It is a faceting of the small ditrigonary icosidodecahedron, using its 20 triangles along with 12 additional pentagons.

It can be constructed as a holosnub great stellated dodecahedron.

This polyhedron is the vertex figure of the great ditrigonary hexacosihecatonicosachoron.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small ditrigonary icosidodecahedron.

Representations

A great ditrigonary icosidodecahedron has the following Coxeter diagrams:

• x3/2o3o5*a
• ß5/2o3o (, as holosnub)

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 3: Quasiregulars" (#35).

• Klitzing, Richard. "gidtid".

• Wikipedia Contributors. "Great ditrigonal icosidodecahedron".
• McCooey, David. "Great Ditrigonal Icosidodecahedron"