m

"M" redirects here. For the Stewart toroid M, see Tortuous tunnel.

m
(3D model)
Rank	3
Type	Acrohedron
Space	Spherical
Notation
Stewart notation	m
Elements
Faces	2 squares, 2+4+4 triangles
Edges	1+2+2+2+4+4+4
Vertices	1+2+2+4
Abstract & topological properties
Flag count	52
Euler characteristic	2
Orientable	Yes
Genus	0
Properties
Symmetry	K2×I, order 4
Convex	No

m is a non-convex polyhedron with regular faces.

Vertex coordinates

Vertex coordinates for m with unit edge length can be given as:

• $\left(\pm\dfrac{1}{2},\,-\sqrt{\dfrac{5-2\sqrt{5}}{20}},\,\pm\sqrt{\dfrac{5+\sqrt{5}}{10}}\right)$,
• $\left(\pm\dfrac{1}{2},\,-\sqrt{\dfrac{5+2\sqrt{5}}{20}},\,0\right)$,
• $\left(\pm\dfrac{1+\sqrt{5}}{4},\,\sqrt{\dfrac{5-\sqrt{5}}{40}},\,0\right)$,
• $\left(0,\,-\sqrt{\dfrac{5-2\sqrt{5}}{5}},\,0\right)$.

Related polytopes

m has 3 concave triangular faces in the same configuration as three faces of the icosahedron. This allows a blend of the icosahedron with m along these faces. Several notable polyhedra are formed as diminishings of this blend.

• 

  m can be blended with the icosahedron.

• 

  m can be blended with J₆₃, a tridiminished icosahedron, to form X.

• 

  m can be augmented by a pentagonal pyramid to form m*, the smallest 5-4-3 acrohedron by face count.

In addition to m*, m is related to another 5-4-3 acrohedron. Two copies of m can be excavated from A₅'' to form the prize substitute, a 5-4-3 acrohedron with 16 faces.

Bibliography

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