R57.16

Statistics

genus c	57, orientable
Schläfli formula c	{6,10}
V / F / E c	48 / 80 / 240
notes
vertex, face multiplicity c	1, 1
Petrie polygons holes 2nd-order Petrie polygons 3rd-order holes 3rd-order Petrie polygons 4th-order holes 4th-order Petrie polygons 5th-order holes 5th-order Petrie polygons	48, each with 10 edges 24, each with 20 edges 40, each with 12 edges 48, each with 10 edges 80, each with 6 edges 40, each with 12 edges 24, each with 20 edges 120, each with 4 edges 120, each with 4 edges
rotational symmetry group	(SL(2,5) ⋊ C2) ⋊ C2, with 480 elements
full symmetry group	960 elements.
its presentation c	< r, s, t | t2, (rs)2, (rt)2, (st)2, r6, srs‑1r3s2r‑2, s10, s3rs‑1r2s3r‑1s  >
C&D number c	R57.16
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is R57.16′.

Its Petrie dual is R73.78.

Its 3-hole derivative is R73.78.

List of regular maps in orientable genus 57.

Other Regular Maps

General Index