Noble enneagrammic icosahedron

Noble enneagrammic icosahedron
(3D model) (OFF file)
Rank	3
Type	Noble
Elements
Faces	20 triangular-symmetric enneagrams
Edges	30+60
Vertices	60
Vertex figure	Isosceles triangle
Measures (edge lengths ${\sqrt {2}}$, ${\frac {5+{\sqrt {5}}}{2}}$)
Edge length ratio	${\frac {5{\sqrt {2}}+{\sqrt {10}}}{4}}\approx 2.55834$
Circumradius	${\frac {\sqrt {11+4{\sqrt {5}}}}{2}}\approx 2.23295$
Central density	5
Number of external pieces	180
Level of complexity	10
Related polytopes
Army	Small rhombicosidodecahedron
Dual	Small noble triangular hexecontahedron
Conjugate	Final stellation of the icosahedron
Convex core	Icosahedron
Abstract & topological properties
Flag count	360
Euler characteristic	–10
Orientable	Yes
Genus	6
Properties
Symmetry	H3, order 120
Flag orbits	3
Convex	No
Nature	Tame
History
Discovered by	Edmond Hess
First discovered	1875

The noble enneagrammic icosahedron or Crennell number 4 stellation of the icosahedron is the conjugate to the final stellation of the icosahedron. It is a noble polyhedron with 20 triangular-symmetric enneagrams for faces. Its convex hull is the uniform small rhombicosidodecahedron.

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