Noble octagonal triacontahedron

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Noble octagonal triacontahedron
Rank3
TypeNoble
Elements
Faces30 rectangular-symmetric octagons
Edges60+60
Vertices60
Vertex figureButterfly
Measures (edge lengths , )
Edge length ratio
Circumradius
Related polytopes
ArmySemi-uniform Ti, edge lengths (pentagons) and 1 (between ditrigons)
DualFirst noble faceting of icosidodecahedron
ConjugateSecond noble octagrammic triacontahedron
Convex coreRhombic triacontahedron
Abstract & topological properties
Flag count480
Euler characteristic–30
OrientableNo
Genus32
Properties
SymmetryH3, order 120
Flag orbits4
ConvexNo
NatureTame
History
Discovered byMax Brückner
First discovered1906

The noble octagonal triacontahedron is a noble polyhedron. Its 30 congruent faces are rectangular-symmetric octagons meeting at congruent order-4 vertices. It is a faceting of the same semi-uniform truncated icosahedron hull as that of the truncated great dodecahedron.

The ratio between the shortest and longest edges is 1: ≈ 1:3.07768.

Vertex coordinates[edit | edit source]

A noble octagonal triacontahedron, centered at the origin, has vertex coordinates given by all permutations of:

  • ,

plus all even permutations of:

  • ,
  • .

These are the same coordinates as the truncated great dodecahedron.