Symbols used in these pages

Thes pages use various symbols to indicate properties of regular maps in a way that takes up little space. Here we explain what these symbols mean.

• Red symbols and letters, indicating that some writers consider the thing not a proper regular map.
  •   The faces do not have at least three edges
  •   The vertices do not have at least three edges
  •   A face shares a vertex with itself, equivalently a vertex shares a face with itself.
  •   A face shares an edge with itself, equivalently an edge shares a face with itself.
  •   An edge shares a vertex with itself, equivalently a vertex shares an edge with itself.
  •   It is not "flag-transitive" with full symmetry including reflection, but chiral
  •   It is not a "polyhedral map"
  •   It is "trivial": its faces have two edges, or its vertices have two edges, or its Petrie polygons have two edges.
• Green symbols and letters, indicating some "positive" property of the regular map.
  •   It is "replete": there is a rotation that fixes one face but not all faces, and a rotation that fixes one vertex but not all vertices.
  •   It is "singular": no pair of vertices, and no pair of faces, has more than one common edge.
  •   It is "cantankerous"^W89.
  •   It is a "polyhedral map"
• cyan letters
  • Rotations of the regular map are all even permutations of its vertices.
  • Some rotations of the regular map are odd permutations of its vertices.
• Blue letters α β γ δ ε ζ η θ ι κ λ μ ν γ with marks ' ° indicating that it is a member of an infinite series of regular maps.

Links to pages about regular maps look like {4,4}_(2,1). Links to pages about not-quite-regular maps look like C5:{10,4}.

A polyhedral map^B97 is such that the valency of each vertex exceeds 2, and the intersection of two distinct faces is one of

• empty
• one vertex
• one edge

Index to Regular Maps
Glossary for Regular Maps