Dual Klein map

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Dual Klein map
Rank3
TypeRegular
Notation
Schläfli symbol{3,7}8
Elements
Faces56 triangles
Edges84
Vertices24
Vertex figureHeptagon
Petrie polygons21 octagons
Holes56 heptagons
Related polytopes
DualKlein map
Abstract & topological properties
Flag count336
Schläfli type{3,7}
OrientableYes
Genus3
Skeleton7-regular Klein graph

The dual Klein map is an abstract regular polyhedron of genus 3. With an automorphism group of order 336 it meets the Hurwitz bound for an orientable surface of genus 3, it along with its dual are the smallest regular polyhedra to meet the Hurwitz bound.

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