Klein map

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Klein map
Rank3
TypeRegular
Notation
Schläfli symbol{7,3}8
Elements
Faces24 heptagons
Edges84
Vertices56
Vertex figureTriangle
Petrie polygons21 octagons
Related polytopes
DualDual Klein map
Petrie dualPetrial Klein map
Abstract & topological properties
Flag count336
Schläfli type{7,3}
OrientableYes
Genus3
SkeletonCubic Klein graph

The 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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