read from main.tex: 6 outlines (hexside with 38 vertices, hexside with 38 vertices, hexside with 38 vertices, hexspoke with 38 vertices, hexspoke with 64 vertices, hexspoke with 64 vertices), 5 punctures
punctures: a = (0.0, 2.7), b = (-2.34, -1.35), c = (2.34, -1.35), tI = (0.0, 0.0), tO = (0.0, -5.4)
t_I inside the triangle abc: True ; t_O inside: False
(0) all six outlines are simple closed polygons; punctures inside: hexside: a,c | hexside: a,b | hexside: b,c | hexspoke: tI,tO | hexspoke: tI,tO | hexspoke: tI,tO
    D_1:  38 vertices, contains exactly a, c
    D_2:  38 vertices, contains exactly tI, tO
    D_3:  38 vertices, contains exactly a, b
    D_4:  64 vertices, contains exactly tI, tO
    D_5:  38 vertices, contains exactly b, c
    D_6:  64 vertices, contains exactly tI, tO
    every label D_j of the figure is nearest to the outline of the disc D_j of the text: True
(H1) consecutive discs
    D_1, D_2: crossings 0, disjoint: True
    D_2, D_3: crossings 0, disjoint: True
    D_3, D_4: crossings 0, disjoint: True
    D_4, D_5: crossings 0, disjoint: True
    D_5, D_6: crossings 0, disjoint: True
    D_6, D_1: crossings 0, disjoint: True
(H2) the nine other pairs; regions as (corners; punctures), * = the unbounded region
    D_1, D_3: transversal True, crossings 2, regions 4: (2; a) (2; b) (2; c) (2; tI,tO)* ; regions with 2 corners and no puncture: 0
    D_1, D_4: transversal True, crossings 4, regions 6: (2; a) (4; b)* (2; c) (2; tI) (2; tO) (4; -) ; regions with 2 corners and no puncture: 0
    D_1, D_5: transversal True, crossings 2, regions 4: (2; a) (2; b) (2; c) (2; tI,tO)* ; regions with 2 corners and no puncture: 0
    D_2, D_4: transversal True, crossings 4, regions 6: (2; a,b)* (2; c) (2; tI) (2; tO) (4; -) (4; -) ; regions with 2 corners and no puncture: 0
    D_2, D_5: transversal True, crossings 4, regions 6: (4; a)* (2; b) (2; c) (2; tI) (2; tO) (4; -) ; regions with 2 corners and no puncture: 0
    D_2, D_6: transversal True, crossings 4, regions 6: (2; a,c)* (2; b) (2; tI) (2; tO) (4; -) (4; -) ; regions with 2 corners and no puncture: 0
    D_3, D_5: transversal True, crossings 2, regions 4: (2; a) (2; b) (2; c) (2; tI,tO)* ; regions with 2 corners and no puncture: 0
    D_3, D_6: transversal True, crossings 4, regions 6: (2; a) (2; b) (4; c)* (2; tI) (2; tO) (4; -) ; regions with 2 corners and no puncture: 0
    D_4, D_6: transversal True, crossings 4, regions 6: (2; a)* (2; b,c) (2; tI) (2; tO) (4; -) (4; -) ; regions with 2 corners and no puncture: 0
(H3) the five sets of Lemma 8.6
    Y = [1, 4]    crossings  4, regions  6, union of curves connected: True, punctures per region: 011111 -> all discs with at most one puncture
    Y = [2, 5]    crossings  4, regions  6, union of curves connected: True, punctures per region: 011111 -> all discs with at most one puncture
    Y = [3, 6]    crossings  4, regions  6, union of curves connected: True, punctures per region: 011111 -> all discs with at most one puncture
    Y = [1, 3, 5] crossings  6, regions  8, union of curves connected: True, punctures per region: 00011111 -> all discs with at most one puncture
    Y = [2, 4, 6] crossings 12, regions 14, union of curves connected: True, punctures per region: 00000000011111 -> all discs with at most one puncture
    D_1, D_3, D_5 have a common point: False ; D_2, D_4, D_6 have a common point: True
all 63 non-empty sets Y: the hypothesis of Lemma 6.3(4) holds for 39 sets and fails for 24;
    it holds exactly for the sets that are not contained in a join of the hexagon: True
Euler characteristic of the cover computed from the regions (regions without puncture lift to d discs, with one to 1):
    Y = [1, 4]    d=5: chi=-10, genus 6 ; d=7: chi=-16, genus 9 ; d=9: chi=-22, genus 12 ; d=15: chi=-40, genus 21
    Y = [2, 5]    d=5: chi=-10, genus 6 ; d=7: chi=-16, genus 9 ; d=9: chi=-22, genus 12 ; d=15: chi=-40, genus 21
    Y = [3, 6]    d=5: chi=-10, genus 6 ; d=7: chi=-16, genus 9 ; d=9: chi=-22, genus 12 ; d=15: chi=-40, genus 21
    Y = [1, 3, 5] d=5: chi=-10, genus 6 ; d=7: chi=-16, genus 9 ; d=9: chi=-22, genus 12 ; d=15: chi=-40, genus 21
    Y = [2, 4, 6] d=5: chi=-10, genus 6 ; d=7: chi=-16, genus 9 ; d=9: chi=-22, genus 12 ; d=15: chi=-40, genus 21
RESULT: ALL CHECKS PASSED
