{4,4}(2,2)

Statistics

genus c1, orientable
Schläfli formula c{4,4}
V / F / E c 8 / 8 / 16
notesreplete singular is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c1, 1
Petrie polygons
holes
2nd-order Petrie polygons
8, each with 4 edges
8, each with 4 edges
8, each with 4 edges
rotational symmetry group((C2×C2)⋊C4)×C2, with 32 elements
full symmetry group64 elements.
C&D number cR1.s2-2
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

It is self-dual.

It is self-Petrie dual.

It can be 2-fold covered to give {4,4}(4,0).
It is a 2-fold cover of {4,4}(2,0).

It can be 3-split to give R9.10′.
It can be 5-split to give R17.13′.
It can be 7-split to give R25.15′.
It can be 9-split to give R33.28′.
It can be 11-split to give R41.15′.

It can be rectified to give {4,4}(4,0).
It is the result of rectifying {4,4}(2,0).

List of regular maps in orientable genus 1.

Wireframe constructions

r {4,4} 2 | 4/2 | 4 × the di-square
rd {4,4} 4/2 | 2 | 4 × the di-square

Underlying Graph

Its skeleton is K4,4.

Cayley Graphs based in this Regular Map


Type I

Q8

Other Regular Maps

General Index

Orientable
sphere | torus | 2 | 3 | 4 | 5 | 6 |
Non-orientable
projective plane | 4 | 5 | 6 | 7 |

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