Final stellation of the rhombic triacontahedron

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Final stellation of the rhombic triacontahedron
Rank3
TypeNoble
Elements
Faces30 rectangular-symmetric dodecagrams
Edges60+60+60
Vertices120
Vertex figureScalene triangle, edge lengths ~1.83181532266 ~2.139581850425 ~1.61249720186
Number of external pieces240
Level of complexity20
Related polytopes
ArmyGrid
DualFirst noble triangular hecatonicosahedron
ConjugateFifth noble stellation of rhombic triacontahedron
Convex coreRhombic triacontahedron
Abstract & topological properties
Flag count720
Euler characteristic–30
OrientableYes
Genus16
Properties
SymmetryH3, order 120
Flag orbits6
ConvexNo
NatureTame
History
Discovered byEdmond Hess
First discovered1876

The final stellation of the rhombic triacontahedron is a noble polyhedron that is a faceting of the uniform great rhombicosidodecahedron. It has 30 rectangular-symmetric dodecagrammic faces.

The ratio between the longest and shortest edges is 1: ≈ 1:1.08576.

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