Noble piscoidal icositetrahedron

Noble piscoidal icositetrahedron
(3D model) (OFF file)
Rank	3
Type	Noble
Elements
Faces	24 mirror-symmetric pentagons
Edges	12+24+24
Vertices	24
Vertex figure	Mirror-symmetric pentagram
Measures (edge lengths ${\sqrt {\frac {2-{\sqrt {2}}}{2}}}$, 1)
Circumradius	${\frac {\sqrt {6-{\sqrt {2}}}}{4}}\approx 0.53536$
Related polytopes
Army	Small rhombicuboctahedron
Dual	Noble pentagrammic icositetrahedron
Conjugate	Noble pentagrammic icositetrahedron
Convex core	Triakis octahedron
Abstract & topological properties
Flag count	240
Euler characteristic	–12
Schläfli type	{5,5}
Orientable	Yes
Genus	7
Properties
Symmetry	B3, order 48
Flag orbits	5
Convex	No
Nature	Tame
History
Discovered by	Edmund Hess
First discovered	1877

The noble faceting of the small rhombicuboctahedron, or the noble piscoidal icositetrahedron, is a noble polyhedron. Its 24 congruent faces are mirror-symmetric pentagons meeting at congruent order-5 vertices.

The ratio between the longest and shortest edges is 1:${\sqrt {2+{\sqrt {2}}}}$ ≈ 1:1.84776.

Vertex coordinates

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