Third noble faceting of icosidodecahedron

Third noble faceting of icosidodecahedron
(3D model) (OFF file)
Rank	3
Type	Noble
Elements
Faces	60 butterflies
Edges	60+60
Vertices	30
Vertex figure	Rectangular-symmetric octagon
Measures (edge lengths ${\sqrt {2}}$, ${\sqrt {\frac {5+{\sqrt {5}}}{2}}}$)
Edge length ratio	${\frac {\sqrt {5+{\sqrt {5}}}}{2}}\approx 1.34500$
Circumradius	$1$
Related polytopes
Army	Id
Dual	Third noble stellation of rhombic triacontahedron
Conjugate	First noble faceting of icosidodecahedron
Convex core	Deltoidal hexecontahedron
Abstract & topological properties
Flag count	480
Euler characteristic	–30
Orientable	No
Genus	32
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame
History
Discovered by	Max Brückner
First discovered	1906

The third 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:${\frac {\sqrt {5+{\sqrt {5}}}}{2}}$ ≈ 1:1.34500.

The butterfly faces are similar to the vertex figure of the small rhombidodecahedron.

Vertex coordinates

Its vertices are the same as those of an icosidodecahedron.