5 vertices:
(3 3) - Isolated.
(1 3) - degree 2
(3 5) - degree 2
(5 3) - degree 2
(3 1) - degree 2
4 edges:
[1 3 3 5]
[3 5 5 3]
[5 3 3 1]
[3 1 1 3]
2 faces:
Unbounded face.
    Hole #1: (1 3)   [1 3 3 5]   (3 5)   [3 5 5 3]   (5 3)   [5 3 3 1]   (3 1)   [3 1 1 3]   (1 3)
Outer boundary: (1 3)   [3 1 1 3]   (3 1)   [5 3 3 1]   (5 3)   [3 5 5 3]   (3 5)   [1 3 3 5]   (1 3)
    Isolated vertex #1: (3 3)
