m
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m  

Rank  3 
Type  Acrohedron 
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 
Measures (edge length 1)  
Volume  
Abstract & topological properties  
Flag count  52 
Euler characteristic  2 
Orientable  Yes 
Genus  0 
Properties  
Symmetry  K_{2}×I, order 4 
Flag orbits  13 
Convex  No 
m is a nonconvex polyhedron with regular faces.
Vertex coordinates[edit  edit source]
Vertex coordinates for m with unit edge length can be given as:
 ,
 ,
 ,
 .
Related polytopes[edit  edit source]
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 augmented by a pentagonal pyramid to form m*,^{[1]} the smallest 543 acrohedron by face count.
In addition to m*, m is related to another 543 acrohedron. Two copies of m can be excavated from A_{5}'' to form the prize substitute, a 543 acrohedron with 16 faces.^{[1]}
References[edit  edit source]
 ↑ ^{1.0} ^{1.1} Stewart (1964:157)
Bibliography[edit  edit source]
 Stewart, Bonnie (1964). Adventures Amoung the Toroids (2 ed.). ISBN 0686119 363.