The initial arrangement:
8 vertices:
(1 3) - degree 3
(5 3) - degree 3
(1 4) - degree 3
(5 4) - degree 3
(1 1) - degree 1
(1 6) - degree 1
(5 1) - degree 1
(5 6) - degree 1
8 edges:
[1 3 5 3]
[1 4 5 4]
[1 1 1 3]
[1 3 1 4]
[1 4 1 6]
[5 1 5 3]
[5 3 5 4]
[5 4 5 6]
2 faces:
Unbounded face.
    Hole #1: (5 4)   [5 3 5 4]   (5 3)   [5 1 5 3]   (5 1)   [5 1 5 3]   (5 3)   [1 3 5 3]   (1 3)   [1 1 1 3]   (1 1)   [1 1 1 3]   (1 3)   [1 3 1 4]   (1 4)   [1 4 1 6]   (1 6)   [1 4 1 6]   (1 4)   [1 4 5 4]   (5 4)   [5 4 5 6]   (5 6)   [5 4 5 6]   (5 4)
Outer boundary: (5 3)   [5 3 5 4]   (5 4)   [1 4 5 4]   (1 4)   [1 3 1 4]   (1 3)   [1 3 5 3]   (5 3)
The final arrangement:
4 vertices:
(1 1) - degree 1
(1 6) - degree 1
(5 1) - degree 1
(5 6) - degree 1
2 edges:
[1 1 1 6]
[5 1 5 6]
1 faces:
Unbounded face.
    Hole #1: (1 6)   [1 1 1 6]   (1 1)   [1 1 1 6]   (1 6)
    Hole #2: (5 1)   [5 1 5 6]   (5 6)   [5 1 5 6]   (5 1)
