First noble octagrammic triacontahedron

First noble octagrammic triacontahedron
(3D model) (OFF file)
Rank	3
Type	Noble
Elements
Faces	30 rectangular-symmetric octagrams
Edges	60+60
Vertices	60
Vertex figure	Butterfly
Measures (edge lengths ${\sqrt {\frac {9+3{\sqrt {5}}}{2}}}$, ${\frac {5+{\sqrt {5}}}{2}}$)
Edge length ratio	${\frac {\sqrt {15}}{5}}\approx 0.77460$
Circumradius	${\sqrt {\frac {21+7{\sqrt {5}}}{8}}}\approx 2.14046$
Related polytopes
Army	Semi-uniform Ti, edge lengths 1 (pentagons) and ${\frac {{\sqrt {5}}-1}{2}}$ (between ditrigons)
Dual	Second noble faceting of icosidodecahedron
Conjugate	First noble octagrammic triacontahedron
Convex core	Rhombic triacontahedron
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 octagrammic triacontahedron is a noble polyhedron. Its 30 congruent faces are rectangular-symmetric octagrams meeting at congruent order-4 vertices. It is a faceting of the same semi-uniform truncated icosahedron hull as that of the rhombidodecadodecahedron.

The ratio between the shortest and longest edges is 1:${\frac {\sqrt {15}}{5}}$ ≈ 1:0.77460.