Fifth noble stellation of rhombic triacontahedron


The fifth 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 great quasitruncated icosidodecahedron.

Fifth noble stellation of rhombic triacontahedron
Rank3
TypeNoble
Elements
Faces30 rectangular-symmetric dodecagrams
Edges60+60+60
Vertices120
Vertex figureScalene triangle
Measures (edge lengths , , )
Edge length ratio
Circumradius
Number of external pieces300
Level of complexity18
Related polytopes
ArmySemi-uniform Grid, edge lengths (dipentagon-rectangle), (dipentagon-ditrigon), (ditrigon-rectangle)
DualFifth noble faceting of icosidodecahedron
ConjugateFinal stellation of the 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 ratio between the shortest and longest edges is 1: ≈ 1:3.97327.

Vertex coordinates edit

A fifth 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 great quasitruncated icosidodecahedron.