Great ditrigonary icosidodecahedron
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Great ditrigonary icosidodecahedron | |
---|---|
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 | |
Volume | |
Dihedral angle | |
Central density | 6 |
Number of pieces | 300 |
Level of complexity | 15 |
Related polytopes | |
Army | Doe |
Regiment | Sidtid |
Dual | Great triambic icosahedron |
Conjugate | Small ditrigonary icosidodecahedron |
Convex core | Dodecahedron |
Abstract properties | |
Euler characteristic | –8 |
Topological properties | |
Orientable | Yes |
Genus | 5 |
Properties | |
Symmetry | H_{3}, 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[edit | edit source]
Its vertices are the same as those of its regiment colonel, the small ditrigonary icosidodecahedron.
Representations[edit | edit source]
A great ditrigonary icosidodecahedron has the following Coxeter diagrams:
- x3/2o3o5*a
- ß5/2o3o (, as holosnub)
Related polyhedra[edit | edit source]
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[edit | edit source]
- Bowers, Jonathan. "Polyhedron Category 3: Quasiregulars" (#35).
- Klitzing, Richard. "gidtid".
- Wikipedia Contributors. "Great ditrigonal icosidodecahedron".
- McCooey, David. "Great Ditrigonal Icosidodecahedron"