Sherk's map

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Sherk's map
Rank3
TypeRegular
Elements
Faces24 squares
Edges48
Vertices16
Vertex figureHexagon
Petrie polygons8 dodecagons
HolesSquares
Related polytopes
φ 2 Cube
Abstract & topological properties
Flag count192
Schläfli type{4,6}
OrientableYes
Genus5

Sherk's map is an orientable abstract regular polyhedron of genus 5.

Realizations[edit | edit source]

Schulte & Wills (1987) give a faithful realization of Sherk's map in 3  on the vertices of two homothetic cubes. This realization is isohedral but not regular.

Related polytopes[edit | edit source]

Sherk's map is a quotient of the mucube.

External links[edit | edit source]

Bibliography[edit | edit source]

  • Schulte, Egon; Wills, Jörg (1987). "Kepler-Poinsot-Type Realizations of Regular Maps of Klein, Fricke, Gordan and Sherk" (PDF). Canadian Math Bulletin. 30.
  • Sherk, F. (1958), The regular maps on a surface of genus three (PDF)