Rhombidodecadodecahedron
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Rhombidodecadodecahedron | |
---|---|
Rank | 3 |
Type | Uniform |
Space | Spherical |
Notation | |
Bowers style acronym | Raded |
Coxeter diagram | x5/2o5x () |
Elements | |
Faces | 30 squares, 12 pentagons, 12 pentagrams |
Edges | 60+60 |
Vertices | 60 |
Vertex figure | Isosceles trapezoid, edge lengths (√5–1)/2, √2, (1+√5)/2, √2 |
Measures (edge length 1) | |
Circumradius | |
Volume | |
Dihedral angles | 4–5/2: |
4–5: | |
Central density | 3 |
Number of pieces | 288 |
Level of complexity | 19 |
Related polytopes | |
Army | Semi-uniform Ti |
Regiment | Raded |
Dual | Medial deltoidal hexecontahedron |
Conjugate | Rhombidodecadodecahedron |
Convex core | Chamfered dodecahedron |
Abstract properties | |
Euler characteristic | -6 |
Topological properties | |
Orientable | Yes |
Genus | 4 |
Properties | |
Symmetry | H_{3}, order 120 |
Convex | No |
Nature | Tame |
The rhombidodecadodecahedron, or raded, is a uniform polyhedron. It consists of 30 squares, 12 pentagons, and 12 pentagrams. One pentagon, one pentagram, and two squares join at each vertex. It can be obtained by cantellation of the small stellated dodecahedron or great dodecahedron, or equivalently by expanding either polyhedron's faces outward and filling in the gaps with appropriate faces.
Vertex coordinates[edit | edit source]
A rhombidodecadodecahedron of edge length 1 has vertex coordinates given by all permutations of
along with all even permutations of
Related polyhedra[edit | edit source]
The rhombidodecadodecahedron is the colonel of a three-member regiment that also includes the icosidodecadodecahedron and the rhombicosahedron.
Oddly, it has the same circumradius as the cuboctatruncated cuboctahedron.
Name | OBSA | Schläfli symbol | CD diagram | Picture |
---|---|---|---|---|
Great dodecahedron | gad | {5,5/2} | x5o5/2o () | |
Truncated great dodecahedron | tigid | t{5,5/2} | x5x5/2o () | |
Dodecadodecahedron | did | r{5,5/2} | o5x5/2o () | |
Truncated small stellated dodecahedron (degenerate, triple cover of doe) | t{5/2,5} | o5x5/2x () | ||
Small stellated dodecahedron | sissid | {5/2,5} | o5o5/2x () | |
Rhombidodecadodecahedron | raded | rr{5,5/2} | x5o5/2x () | |
Truncated dodecadodecahedron (degenerate, sird+12(10/2)) | tr{5,5/2} | x5x5/2x () | ||
Snub dodecadodecahedron | siddid | sr{5,5/2} | s5s5/2s () |
External links[edit | edit source]
- Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#42).
- Klitzing, Richard. "raded".
- Wikipedia Contributors. "Rhombidodecadodecahedron".
- McCooey, David. "Rhombidodecadodecahedron"