S4:{10,10}

Statistics

genus c	4, orientable
Schläfli formula c	{10,10}
V / F / E c	2 / 2 / 10
notes
vertex, face multiplicity c	10, 10
Petrie polygons holes 2nd-order Petrie polygons 3rd-order holes 3rd-order Petrie polygons 4th-order holes 4th-order Petrie polygons 5th-order Petrie polygons	10, each with 2 edges 2, each with 10 edges 10, each with 2 edges 2, each with 10 edges 10, each with 2 edges 2, each with 10 edges 10, each with 2 edges 10, each with 2 edges
rotational symmetry group	C5×C2×C2, with 20 elements
full symmetry group	D20×C2, with 40 elements
its presentation c	< r, s, t | t2, sr2s, (r, s), (rt)2, (st)2, r‑2tr6tr‑2 >
C&D number c	R4.11
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 its own 3-hole derivative.

It is a member of series k.

List of regular maps in orientable genus 4.

Wireframe constructions

	×	S2:{10,5}		unconfirmed
	×	S2:{10,5}
	×	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