m*

m*
(3D model)
Rank	3
Type	Acrohedron
Notation
Stewart notation	m*
Elements
Faces	1+2+2+2+2 triangles, 1+1 squares, 1 pentagon
Edges	20
Vertices	10
Measures (edge length 1)
Volume	${\frac {9+5{\sqrt {5}}}{24}}\approx 0.84085$
Surface area	${\frac {8+9{\sqrt {3}}+{\sqrt {25+10{\sqrt {5}}}}}{4}}$
Abstract & topological properties
Flag count	80
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	A1×I×I, order 2
Flag orbits	40
Convex	No
Nature	Tame

m* is a nonconvex polyhedron with all regular faces, and the smallest known non-self-intersecting 5-4-3 acrohedron. It was first described and named by Bonnie Stewart in Adventures Among the Toroids, and rediscovered during the search for acrohedra. It can be formed as an outer-blend of m with a pentagonal pyramid.

External links

• Jim McNeill. "5-4-3"

Bibliography

• Stewart, Bonnie (1964). Adventures Amoung the Toroids (2 ed.). ISBN 0686-119 36-3.