{4,4}(2,0)

Statistics

genus c1, orientable
Schläfli formula c{4,4}
V / F / E c 4 / 4 / 8
notesreplete is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c2, 2
Petrie polygons
holes
4, each with 4 edges
8, each with 2 edges
rotational symmetry group(C2×C2) ⋊ C4, with 16 elements
full symmetry group32 elements.
C&D number cR1.s2-0
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}(2,2).
It is a 2-fold cover of {4,4}(1,1).

It can be 3-split to give S5:{12,4}.
It can be 5-split to give R9.12′.
It can be 7-split to give R13.6′.
It can be 9-split to give R17.14′.
It can be 11-split to give R21.12′.

It can be rectified to give {4,4}(2,2).
It is the result of rectifying {4,4}(1,1).

It is a member of series l.
It is a member of series m.

List of regular maps in orientable genus 1.

Wireframe constructions

p  {4,4}  2 | 4/2 | 4 × the 2-hosohedron
pd  {4,4}  4/2 | 2 | 4 × the 2-hosohedron
q  {4,4}  2 | 4/2 | 4 × the 2-hosohedron
qd  {4,4}  4/2 | 2 | 4 × the 2-hosohedron
r  {4,4}  2 | 4/2 | 4 × the 2-hosohedron
rd  {4,4}  4/2 | 2 | 4 × the 2-hosohedron
t  {4,4}  2 | 4/2 | 4 × the 2-hosohedron With a Dehn twist
td  {4,4}  4/2 | 2 | 4 × the 2-hosohedron With a Dehn twist.

Underlying Graph

Its skeleton is 2 . 4-cycle.

Cayley Graphs based in this Regular Map


Type I

C2×C2

Type II

(C2×C2) ⋊ C4

Type IIa

(C2×C2) ⋊ C4

Other Regular Maps

General Index

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