Sixth noble stellation of rhombic triacontahedron
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Sixth noble stellation of rhombic triacontahedron | |
---|---|
Rank | 3 |
Type | Noble |
Elements | |
Faces | 30 rectangular-symmetric dodecagrams |
Edges | 60+60+60 |
Vertices | 120 |
Vertex figure | Scalene triangle |
Measures (edge lengths , , ) | |
Edge length ratio | |
Circumradius | |
Number of external pieces | 1020 |
Level of complexity | 54 |
Related polytopes | |
Army | Semi-uniform Grid, edge lengths (decagons), (ditrigon-rectangle) |
Dual | Sixth noble faceting of icosidodecahedron |
Conjugate | Sixth noble stellation of rhombic triacontahedron |
Convex core | Rhombic triacontahedron |
Abstract & topological properties | |
Flag count | 720 |
Euler characteristic | –30 |
Orientable | Yes |
Genus | 16 |
Properties | |
Symmetry | H3, order 120 |
Flag orbits | 6 |
Convex | No |
Nature | Tame |
The sixth noble stellation of rhombic triacontahedron is a noble polyhedron. Its 30 congruent faces are rectangular-symmetric dodecagrams meeting at congruent order-3 vertices. It is a faceting of the same semi-uniform great rhombicosidodecahedron hull as that of the quasitruncated dodecadodecahedron.
The ratio between the shortest and longest edges is 1: ≈ 1:4.23607.
Vertex coordinates[edit | edit source]
A sixth noble stellation of rhombic triacontahedron, centered at the origin, has vertex coordinates given by all permutations of
- ,
- ,
along with all even permutations of:
- ,
- ,
- .
These are the same coordinates as the quasitruncated dodecadodecahedron.