Inverted snub dodecadodecahedron
The inverted snub dodecadodecahedron or isdid, is a uniform polyhedron. It consists of 60 snub triangles, 12 pentagrams, and 12 pentagons. Three triangles, 1 pentagon, and one pentagram meeting at each vertex. It can be constructed by alternation of the quasitruncated dodecadodecahedron and then setting all edge lengths to be equal.
Inverted snub dodecadodecahedron | |
---|---|
Rank | 3 |
Type | Uniform |
Space | Spherical |
Notation | |
Bowers style acronym | Isdid |
Coxeter diagram | s5/3s5s () |
Elements | |
Faces | 60 triangles, 12 pentagons, 12 pentagrams |
Edges | 60+60+30 |
Vertices | 60 |
Vertex figure | Irregular pentagon, edge lengths 1, 1, (√5–1)/2, 1, (1+√5)/2 |
Measures (edge length 1) | |
Circumradius | ≈ 0.85163 |
Volume | ≈ 4.61431 |
Dihedral angles | 3–3: ≈ 130.49074° |
5–3: ≈ 68.64088° | |
5/2–3: ≈ 11.12448° | |
Central density | 9 |
Number of pieces | 372 |
Level of complexity | 39 |
Related polytopes | |
Army | Non-uniform snid |
Regiment | Isdid |
Dual | Medial inverted pentagonal hexecontahedron |
Conjugate | Snub dodecadodecahedron |
Convex core | Dodecahedron |
Abstract properties | |
Euler characteristic | -6 |
Topological properties | |
Orientable | Yes |
Properties | |
Symmetry | H_{3}+, order 60 |
Convex | No |
Nature | Tame |
MeasuresEdit
The circumradius R ≈ 0.85163 of the inverted snub dodecadodecahedron with unit edge length is the smallest positive real root of:
Its volume V ≈ 4.61431 is given by the smallest positive real root of:
These same polynomials define the circumradius and volume of the snub dodecadodecahedron.
Related polyhedraEdit
The inverted disnub dodecadodecahedron is a uniform polyhedron compound composed of the 2 opposite chiral forms of the inverted snub dodecadodecahedron.
Name | OBSA | Schläfli symbol | CD diagram | Picture |
---|---|---|---|---|
Small stellated dodecahedron | sissid | {5/3,5} | x5/3o5o ( ) | |
Quasitruncated small stellated dodecahedron | quit sissid | t{5/3,5} | x5/3x5o ( ) | |
Dodecadodecahedron | did | r{5,5/3} | o5/3x5o ( ) | |
Truncated great dodecahedron | tigid | t{5,5/3} | o5/3x5x ( ) | |
Great dodecahedron | gad | {5,5/3} | o5/3o5x ( ) | |
Complex ditrigonal rhombidodecadodecahedron (degenerate, ditdid+rhom) | cadditradid | rr{5,5/3} | x5/3o5x ( ) | |
Quasitruncated dodecadodecahedron | quitdid | tr{5,5/3} | x5/3x5x ( ) | |
Inverted snub dodecadodecahedron | isdid | sr{5,5/3} | s5/3s5s ( ) |
External linksEdit
- Bowers, Jonathan. "Polyhedron Category 6: Snubs" (#69).
- Klitzing, Richard. "isdid".
- Wikipedia Contributors. "Inverted snub dodecadodecahedron".
- McCooey, David. "Inverted Snub Dodecadodecahedron"