S(5)
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S(5)

Again we use the regular representation of a small group. Is there some embedding without self-intersections as well? Probably.

Figure 7.21. S(5)

here a snapshot should be displayed

S(5) as a compact Riemann surface of orbit genus 4 (with some self-intersections)


vertices: 24
faces: 30
edges: 60
genus: 4

characteristic polynomial: (x - 5) (x - 1) (x + 1) (x + 5) (x2 - 5)6

dual's characteristic polynomial: (x - 4) (x - 2)11 x5 (x + 1)4 (x + 2)5 (x + 3)4

chromatic number: 3

lattice group: A(5):Z(2) ≅ S(5)

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