connected dominating vertex sets of Lambda = C_5: 11 [[1, 2, 3], [1, 2, 5], [1, 4, 5], [2, 3, 4], [3, 4, 5], [1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 4, 5], [1, 3, 4, 5], [2, 3, 4, 5], [1, 2, 3, 4, 5]]
genus of the cover: 6 ; chi = -10
X_1: connected True, chi -3, boundary components 1, genus 2, xi 4 ; complement: 1 component(s), chi [-7]
X_2: connected True, chi -3, boundary components 1, genus 2, xi 4 ; complement: 1 component(s), chi [-7]
X_3: connected True, chi -3, boundary components 1, genus 2, xi 4 ; complement: 1 component(s), chi [-7]
X_4: connected True, chi -3, boundary components 1, genus 2, xi 4 ; complement: 1 component(s), chi [-7]
X_5: connected True, chi -3, boundary components 1, genus 2, xi 4 ; complement: 1 component(s), chi [-7]
pair (1,2) consecutive: regions of the two lifted curves as (chi, corners): [(-3, 10), (1, 10), (1, 10), (1, 10)]
pair (1,3) far: regions of the two lifted curves as (chi, corners): [(-4, 0), (-3, 0), (-3, 0)]
pair (1,4) far: regions of the two lifted curves as (chi, corners): [(-4, 0), (-3, 0), (-3, 0)]
pair (1,5) consecutive: regions of the two lifted curves as (chi, corners): [(-3, 10), (1, 10), (1, 10), (1, 10)]
pair (2,3) consecutive: regions of the two lifted curves as (chi, corners): [(-3, 10), (1, 10), (1, 10), (1, 10)]
pair (2,4) far: regions of the two lifted curves as (chi, corners): [(-4, 0), (-3, 0), (-3, 0)]
pair (2,5) far: regions of the two lifted curves as (chi, corners): [(-4, 0), (-3, 0), (-3, 0)]
pair (3,4) consecutive: regions of the two lifted curves as (chi, corners): [(-3, 10), (1, 10), (1, 10), (1, 10)]
pair (3,5) far: regions of the two lifted curves as (chi, corners): [(-4, 0), (-3, 0), (-3, 0)]
pair (4,5) consecutive: regions of the two lifted curves as (chi, corners): [(-3, 10), (1, 10), (1, 10), (1, 10)]
Y = (1, 2, 3) : regions 10, all discs: True
Y = (1, 2, 5) : regions 10, all discs: True
Y = (1, 4, 5) : regions 10, all discs: True
Y = (2, 3, 4) : regions 10, all discs: True
Y = (3, 4, 5) : regions 10, all discs: True
Y = (1, 2, 3, 4) : regions 20, all discs: True
Y = (1, 2, 3, 5) : regions 20, all discs: True
Y = (1, 2, 4, 5) : regions 20, all discs: True
Y = (1, 3, 4, 5) : regions 20, all discs: True
Y = (2, 3, 4, 5) : regions 20, all discs: True
Y = (1, 2, 3, 4, 5) : regions 40, all discs: True

PENDANT (p attached to vertex 1; U_p = S - U_1):
  regions of dU_1 u dU_2 inside U_1: chi = [1, 1]  (all discs: True)
  regions of dU_1 u dU_5 inside U_1: chi = [1, 1]  (all discs: True)
TRIANGLE ON AN EDGE (q adjacent to 1 and 3; U_q = S - U_1 - U_3):
  S - U_1 - U_3: 1 component(s), chi [-4] -> with 2 boundary curves: genus [2]
  regions of dU_1 u dU_2 inside U_1: chi = [1, 1] (all discs: True)
  regions of dU_3 u dU_2 inside U_3: chi = [1, 1] (all discs: True)
  regions of dU_3 u dU_4 inside U_3: chi = [1, 1] (all discs: True)
  regions of dU_1 u dU_5 inside U_1: chi = [1, 1] (all discs: True)
