genus c1, orientable
Schläfli formula c{4,4}
V / F / E c 5 / 5 / 10
notesChiral replete singular is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c1, 1
Petrie polygons
2, each with 10 edges
4, each with 5 edges
antipodal sets5 of ( v, f ), 5 of ( 2e )
rotational symmetry groupFrob(20), with 20 elements
full symmetry groupFrob(20), with 20 elements
C&D number cC1.s2-1
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

It is self-dual.

Its Petrie dual is C5:{10,4}.

It can be 2-fold covered to give {4,4}(3,1).

It can be rectified to give {4,4}(3,1).

List of regular maps in orientable genus 1.

Underlying Graph

Its skeleton is K5.


Its graph is the the same as that of the 4-simplex.

When I was in Amiens cathedral and saw the staircase pictured to the right, I was reminded of this regular map. Though now that I see them together, there is little resemblance.

Cayley Graphs based in this Regular Map

Type II


Other Regular Maps

General Index

The images on this page are copyright © 2010 N. Wedd