# m

m Rank3
TypeAcrohedron
SpaceSpherical
Notation
Stewart notationm
Elements
Faces2 squares, 2+4+4 triangles
Edges1+2+2+2+4+4+4
Vertices1+2+2+4
Abstract & topological properties
Flag count52
Euler characteristic2
OrientableYes
Genus0
Properties
SymmetryK2×I, order 4
ConvexNo

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.

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.