Great dodecicosidodecahedron
The great dodecicosidodecahedron, or gaddid, is a uniform polyhedron. It consists of 20 triangles, 12 pentagrams, and 12 decagrams. One triangle, one pentagram, and two decagrams join at each vertex.
Great dodecicosidodecahedron | |
---|---|
Rank | 3 |
Type | Uniform |
Space | Spherical |
Notation | |
Bowers style acronym | Gaddid |
Coxeter diagram | x5/3x5/2o3*a () |
Elements | |
Faces | 20 triangles, 12 pentagrams, 12 decagrams |
Edges | 60+60 |
Vertices | 60 |
Vertex figure | Isosceles trapezoid, edge lengths 1, √(5–√5)/2, (√5–1)/2, √(5–√5)/2 |
Measures (edge length 1) | |
Circumradius | |
Volume | |
Dihedral angles | 5/2–10/3: |
3–10/3: | |
Central density | 10 |
Number of external pieces | 180 |
Level of complexity | 13 |
Related polytopes | |
Army | Semi-uniform Ti, edge lengths (pentagons), (between ditrigons) |
Regiment | Gaddid |
Dual | Great dodecacronic hexecontahedron |
Conjugate | Small dodecicosidodecahedron |
Convex core | Truncated dodecahedron |
Abstract & topological properties | |
Flag count | 480 |
Euler characteristic | –16 |
Orientable | Yes |
Properties | |
Symmetry | H_{3}, order 120 |
Convex | No |
Nature | Tame |
Vertex coordinatesEdit
A great dodecicosidodecahedron of edge length 1 has vertex coordinates given by all permutations of
along with all even permutations of
Related polyhedraEdit
The great dodecicosidodecahedron is the colonel of a three-member regiment that also includes the quasirhombicosidodecahedron and the great rhombidodecahedron.
Name | OBSA | CD diagram | Picture |
---|---|---|---|
Great complex icosidodecahedron (degenerate, sissid+gike) | gacid | x5/3o5/2o3*a ( ) | |
Great dodecicosidodecahedron | gaddid | x5/3x5/2o3*a ( ) | |
(degenerate, double cover of gissid) | o5/3x5/2o3*a ( ) | ||
(degenerate, ditdid+gidtid) | o5/3x5/2x3*a ( ) | ||
Great complex icosidodecahedron (degenerate, sissid+gike) | gacid | o5/3o5/2x3*a ( ) | |
(degenerate, double cover of sidhei) | x5/3o5/2x3*a ( ) | ||
(degenerate, giddy+12(10/2)) | x5/3x5/2x3*a ( ) | ||
Great snub dodecicosidodecahedron | gisdid | s5/3s5/2s2*a ( ) |
External linksEdit
- Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#54).
- Klitzing, Richard. "gaddid".
- Wikipedia Contributors. "Great dodecicosidodecahedron".
- McCooey, David. "Great Dodecicosidodecahedron"