Second noble faceting of icosidodecahedron

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Second noble faceting of icosidodecahedron
Rank3
TypeNoble
Elements
Faces60 butterflies
Edges60+60
Vertices30
Vertex figureRectangular-symmetric octagon
Measures (edge lengths , )
Edge length ratio
Circumradius
Related polytopes
ArmyId
DualSecond noble stellation of rhombic triacontahedron
ConjugateSecond noble faceting of icosidodecahedron
Convex coreNon-Catalan pentakis dodecahedron
Abstract & topological properties
Flag count480
Euler characteristic–30
OrientableNo
Genus32
Properties
SymmetryH3, order 120
ConvexNo
NatureTame
History
Discovered byMax Brückner
First discovered1906


The second noble faceting of icosidodecahedron is a noble polyhedron. Its 60 congruent faces are butterflies meeting at congruent order-8 vertices. It is a faceting of a uniform icosidodecahedron hull.

The ratio between the shortest and longest edges is 1: ≈ 1:1.22474.

The butterfly faces are similar to the vertex figure of the rhombicosahedron.

Vertex coordinates[edit | edit source]

Its vertices are the same as those of an icosidodecahedron.