S4:{10,10}

Statistics

genus c4, orientable
Schläfli formula c{10,10}
V / F / E c 2 / 2 / 10
notesFaces share vertices with themselves trivial is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c10, 10
Petrie polygons
holes
2nd-order Petrie polygons
3rd-order holes
3rd-order Petrie polygons
10, each with 2 edges
2 double, each with 10 edges
10, each with 2 edges
2 Eulerian, each with 10 edges
10, each with 2 edges
rotational symmetry groupC5×C2×C2, with 20 elements
full symmetry groupD20×C2, with 40 elements
its presentation c< r, s, t | t2, sr2s, (r, s), (rt)2, (st)2, r‑2tr6tr‑2 >
C&D number cR4.11
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 the 10-hosohedron.

It can be built by 2-splitting S2:{5,10}.

It can be rectified to give S4:{10,4}.

It is a member of series k.

List of regular maps in orientable genus 4.

Wireframe constructions

x  {10,10}  2/5 | 2/5 | 2 × S2:{10,5} unconfirmed
y  {10,10}  2/5 | 2/5 | 2 × S2:{10,5}
z  {10,10}  2/5 | 2/5 | 2 × the 5-hosohedron

Underlying Graph

Its skeleton is 10 . K2.

Other Regular Maps

General Index

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