First noble faceting of icosidodecahedron
(Redirected from Noble faceting of icosidodecahedron 1)
First noble faceting of icosidodecahedron | |
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Rank | 3 |
Type | Noble |
Elements | |
Faces | 60 butterflies |
Edges | 60+60 |
Vertices | 30 |
Vertex figure | Rectangular-symmetric octagon |
Measures (edge lengths , ) | |
Edge length ratio | |
Circumradius | |
Related polytopes | |
Army | Id |
Dual | First noble stellation of rhombic triacontahedron |
Conjugate | Third noble faceting of icosidodecahedron |
Convex core | Non-Catalan pentakis dodecahedron |
Abstract & topological properties | |
Flag count | 480 |
Euler characteristic | –30 |
Orientable | No |
Genus | 32 |
Properties | |
Symmetry | H3, order 120 |
Flag orbits | 4 |
Convex | No |
Nature | Tame |
History | |
Discovered by | Max Brückner |
First discovered | 1906 |
The first 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: ≈ 1:1.20300.
The butterfly faces are similar to the vertex figure of the great rhombidodecahedron.
Vertex coordinates[edit | edit source]
Its vertices are the same as those of an icosidodecahedron.