R9.12

Statistics

genus c	9, orientable
Schläfli formula c	{4,20}
V / F / E c	4 / 20 / 40
notes
vertex, face multiplicity c	10, 2
Petrie polygons holes 2nd-order Petrie polygons 3rd-order holes 3rd-order Petrie polygons 6th-order holes 6th-order Petrie polygons 7th-order holes 7th-order Petrie polygons 9th-order holes 9th-order Petrie polygons	4, each with 20 edges 40, each with 2 edges 8, each with 10 edges 20, each with 4 edges 4, each with 20 edges 40, each with 2 edges 8, each with 10 edges 20, each with 4 edges 4, each with 20 edges 20, each with 4 edges 4, each with 20 edges
rotational symmetry group	80 elements.
full symmetry group	160 elements.
its presentation c	< r, s, t | t2, r4, (rs)2, (rs‑1)2, (rt)2, (st)2, s20  >
C&D number c	R9.12
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is R9.12′.

Its Petrie dual is R17.37.

It can be 3-split to give R45.28.
It can be 5-split to give R81.145.

It is its own 3-hole derivative.
It is its own 7-hole derivative.
It is its own 9-hole derivative.

It is a member of series θ.

List of regular maps in orientable genus 9.

Wireframe constructions

	×	the 10-hosohedron
	×	the 10-hosohedron

Other Regular Maps

General Index