First noble octagrammic triacontahedron

First noble octagrammic triacontahedron
(3D model) (OFF file)
Rank	3
Type	Noble
Space	Spherical
Elements
Faces	30 rectangular-symmetric octagrams
Edges	120
Vertices	60
Vertex figure	Butterfly
Measures (edge lengths $\sqrt{\frac{9+3\sqrt5}{2}}$, $\frac{5+\sqrt5}{2}$)
Edge length ratio	$\frac{\sqrt{15}}{5} \approx 0.77460$
Circumradius	$\sqrt{\frac{21+7\sqrt5}{8}} \approx 2.14046$
Related polytopes
Army	Semi-uniform Ti, edge lengths 1 (pentagons) and $\frac{\sqrt5-1}{2}$ (between ditrigons)
Dual	Second noble faceting of icosidodecahedron
Convex core	Rhombic triacontahedron
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 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 a semi-uniform truncated icosahedron hull.

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