R19.23

Statistics

genus c19, orientable
Schläfli formula c{7,7}
V / F / E c 24 / 24 / 84
notesreplete singular
vertex, face multiplicity c1, 1
Petrie polygons
28, each with 6 edges
rotational symmetry group168 elements.
full symmetry group336 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 cR19.23
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′.

It can be derived by stellation (with path <>/2) from S3:{3,7}. The density of the stellation is 3.
It can be derived by stellation (with path <1,-1>) from S3:{3,7}. The density of the stellation is 3.
It can be derived by stellation (with path <2,-2>) from S3:{3,7}. 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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