R19.23

Statistics

genus ^c	19, orientable
Schläfli formula ^c	{7,7}
V / F / E ^c	24 / 24 / 84
notes
vertex, face multiplicity ^c	1, 1
Petrie polygons holes 2nd-order Petrie polygons 3rd-order holes 3rd-order Petrie polygons	28, each with 6 edges 42, each with 4 edges 21, each with 8 edges 56, each with 3 edges 21, each with 8 edges
rotational symmetry group	PSL(3,2) , with 168 elements
full symmetry group	336 elements.
its presentation ^c	< r, s, t \| t², (rs)², (rt)², (st)², r^‑7, (rs^‑1)⁴, s^‑7, (r^‑2s)³ >
C&D number ^c	R19.23
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 N34.5.

It can be 2-split to give R49.58′.

It can be rectified to give R19.4′.

Its 2-hole derivative is R10.9.
Its 3-hole derivative is the dual Klein map.

It can be derived by stellation (with path <>/2) from the dual Klein map. The density of the stellation is 3.
It can be derived by stellation (with path <1,-1>) from the dual Klein map. The density of the stellation is 3.
It can be derived by stellation (with path <2,-2>) from the dual Klein map. The density of the stellation is 9.

List of regular maps in orientable genus 19.

Comments

This regular map can be derived from the dual of the Klein map in the same way that S4:{5,5} can be derived from the icosahedron. S4:{5,5} is known, when immersed in the sphere (or in 3-space), as the great dodecahedron, and with a different immersion, as the small stellated dodecahedron. So this regular map might analogously be called "the great Klein map", and regarded as a stellation (in fact three stellations, differently immersed in the genus-3 surface) of the Klein map.

Other Regular Maps

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