S4:{10,4}

Statistics

genus c4, orientable
Schläfli formula c{10,4}
V / F / E c 10 / 4 / 20
notesreplete is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c2, 5
Petrie polygons
holes
2nd-order Petrie polygons
2, each with 20 edges
20, each with 2 edges
20, each with 2 edges
rotational symmetry group40 elements.
full symmetry group80 elements.
its presentation c< r, s, t | t2, s4, (sr)2, (sr‑1)2, (st)2, (rt)2, r10 >
C&D number cR4.4′
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S4:{4,10}.

Its Petrie dual is S5:{20,4}.

It can be 3-split to give R14.4′.
It can be 7-split to give R34.4′.
It can be 9-split to give R44.1′.
It can be 11-split to give R54.2′.

It is the result of rectifying S4:{10,10}.

It is a member of series l.

List of regular maps in orientable genus 4.

Wireframe constructions

p {10,4} 2 | 4/5 | 4 × the 5-hosohedron
q {10,4} 2 | 4/5 | 4 × the 5-hosohedron
t {10,4} 2 | 4/5 | 4 × S2:{10,5}

Underlying Graph

Its skeleton is 2 . 10-cycle.

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