First noble triangular hecatonicosahedron

First noble triangular hecatonicosahedron
(3D model) (OFF file)
Rank	3
Type	Noble
Elements
Faces	120 scalene triangles
Edges	60+60+60
Vertices	30
Vertex figure	Rectangular-symmetric dodecagram
Measures (edge lengths ${\sqrt {2}}$, ${\sqrt {3}}$, ${\sqrt {\frac {5+{\sqrt {5}}}{2}}}$)
Circumradius	$1$
Number of external pieces	1080
Level of complexity	74
Related polytopes
Army	Id
Dual	Final stellation of the rhombic triacontahedron
Conjugate	Second noble triangular hecatonicosahedron
Convex core	Disdyakis triacontahedron
Abstract & topological properties
Flag count	720
Euler characteristic	–30
Orientable	Yes
Genus	16
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame
History
Discovered by	Edmond Hess
First discovered	1876

The first noble triangular hecatonicosahedron is a noble polyhedron. Its 120 congruent faces are scalene triangles meeting at congruent order-12 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 triangular faces are similar to the vertex figure of the great rhombicosidodecahedron.

Vertex coordinates

Its vertices are the same as those of an icosidodecahedron.