Regular Maps

Index to the diagrams of regular maps

• • The sphere. The five regular polyhedra, and an infinite series of dual pairs of regular maps not regarded as polyhedra. Thirty-three shown.
  • The torus. An infinite set of self-dual regular maps, and an infinite set of dual pairs of regular maps. Sixty-eight shown.
  • The genus-2 orientable manifold. Ten regular maps: four dual pairs and two self-duals. All ten shown.
  • The genus-3 orientable manifold. Twenty regular maps: eight dual pairs and four self-duals. All twenty shown.
  • The genus-4 orientable manifold. Twenty regular maps: eight dual pairs and four self-duals. All twenty shown.
  • The genus-5 orientable manifold. Twenty-six regular maps: ten dual pairs and six self-duals. Ten shown.
  • The genus-6 orientable manifold. Twenty-three regular maps: ten dual pairs and three self-duals. Ten shown.
• • The projective plane. The four regular hemi-polyhedra, and an infinite series of dual pairs of regular maps. Seventeen shown.
  • No regular map exists in the Klein bottle.
  • No regular map exists in the genus-3 non-orientable surface.
  • The genus-4 non-orientable surface. Four regular maps, in two dual pairs. All four shown.
  • The genus-5 non-orientable surface. Six regular maps: two dual pairs and two self-dual. All six shown.
  • The genus-6 non-orientable surface. Six regular maps, in three dual pairs. All six shown.
  • The genus-7 non-orientable surface. Four regular maps, in two dual pairs. Two shown.