Third noble unihexagrammic hexecontahedron

Third noble unihexagrammic hexecontahedron
(3D model) (OFF file)
Rank	3
Type	Noble
Elements
Faces	60 unicursal hexagrams
Edges	60+120
Vertices	60
Vertex figure	Irregular hexagon
Measures (edge lengths ${\frac {5+{\sqrt {5}}}{2}}$, ${\sqrt {10+4{\sqrt {5}}}}$)
Edge length ratio	${\sqrt {\frac {5+{\sqrt {5}}}{5}}}\approx 1.20300$
Circumradius	${\frac {\sqrt {11+4{\sqrt {5}}}}{2}}\approx 2.23295$
Number of external pieces	1680
Related polytopes
Army	Srid
Dual	First noble ditrapezoidal hexecontahedron
Conjugate	First noble ditrapezoidal hexecontahedron
Convex core	Non-Catalan Pentakis dodecahedron
Abstract & topological properties
Flag count	720
Euler characteristic	–60
Orientable	Yes
Genus	31
Properties
Symmetry	H3, order 120
Flag orbits	6
Convex	No
Nature	Tame

The third noble unihexagrammic hexecontahedron is a noble polyhedron. Its 60 congruent faces are rectangular-symmetric unicursal hexagrams meeting at congruent order-6 vertices. It is a faceting of a uniform small rhombicosidodecahedron hull.

The ratio between the shortest and longest edges is 1:${\sqrt {\frac {5+{\sqrt {5}}}{5}}}$ ≈ 1:1.20300.

Vertex coordinates

Its vertices are the same as those of a small rhombicosidodecahedron.