{4,4}(4,0)

Statistics

genus c1, orientable
Schläfli formula c{4,4}
V / F / E c 16 / 16 / 32
notesreplete singular is a polyhedral map permutes its vertices oddly
vertex, face multiplicity c1, 1
Petrie polygons
holes
8, each with 8 edges
16, each with 4 edges
rotational symmetry group(C4×C4)⋊C4, with 64 elements
full symmetry group128 elements.
C&D number cR1.s4-0
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 S5:{8,4}4.

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

It can be 3-split to give R17.12′.
It can be 5-split to give R33.25′.
It can be 7-split to give R49.28′.
It can be 9-split to give R65.44′.
It can be 11-split to give R81.30′.

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

List of regular maps in orientable genus 1.

Underlying Graph

Its skeleton is C4 □ C4.

Comments

Its graph is the the same as that of the tesseract.

Cayley Graphs based in this Regular Map


Type I

C4 ⋊ C4
D8×C2
C4×C4
C2×C2×C2×C2
C4×C2×C2

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