# m

m
Rank3
TypeAcrohedron
Notation
Stewart notationm
Elements
Faces2 squares, 2+4+4 triangles
Edges1+2+2+2+4+4+4
Vertices1+2+2+4
Measures (edge length 1)
Volume${\displaystyle {\frac {1+{\sqrt {5}}}{6}}\approx 0.53934}$
Abstract & topological properties
Flag count52
Euler characteristic2
OrientableYes
Genus0
Properties
SymmetryK2×I, order 4
Flag orbits13
ConvexNo

m is a non-convex polyhedron with regular faces.

## Vertex coordinates

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

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

## 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.

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.[1]

## References

1. Stewart (1964:157)

## Bibliography

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