Great icosicosidodecahedron
(Redirected from Giid)
Great icosicosidodecahedron | |
---|---|
Rank | 3 |
Type | Uniform |
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 | |
Volume | |
Dihedral angles | 5–6: |
3–6: | |
Central density | 6 |
Number of external pieces | 1232 |
Level of complexity | 75 |
Related polytopes | |
Army | Tid, edge length |
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[edit | edit source]
Its vertices are the same as those of its regiment colonel, the great ditrigonal dodecicosidodecahedron.
Related polyhedra[edit | edit source]
External links[edit | edit source]
- Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#49).
- Klitzing, Richard. "giid".
- Wikipedia contributors. "Great icosicosidodecahedron".
- McCooey, David. "Great Icosicosidodecahedron"