Dénombrement du nombre de rectangles

class Point:
    """Représente un point géométrique du plan"""

    def __init__(self, x: int, y: int, name: str):
        self.x = x
        self.y = y
        self.name = name

    def __eq__(self, other):
        return self.x == other.x and self.y == other.y

    def __hash__(self):
        return hash((self.x, self.y))

    def __repr__(self):
        return self.name

## Définition des points et de leurs voisins

A = Point(0, 5, "A")
B = Point(1, 5, "B")
C = Point(3, 5, "C")
D = Point(4, 5, "D")
E = Point(6, 5, "E")

F = Point(0, 3, "F")
G = Point(1, 3, "G")
H = Point(3, 3, "H")
I = Point(4, 3, "I")
J = Point(6, 3, "J")

K = Point(2, 4, "K")
L = Point(3, 4, "L")
M = Point(4, 4, "M")
N = Point(5, 4, "N")

O = Point(2, 3, "O")
P = Point(5, 3, "P")

Q = Point(2, 1, "Q")
R = Point(3, 1, "R")
S = Point(5, 1, "S")

T = Point(4, 2, "T")
U = Point(5, 2, "U")

V = Point(1, 6, "V")
W = Point(3, 6, "W")

X = Point(4, 7, "X")
Y = Point(7, 7, "Y")

Z = Point(7, 2, "Z")

AA = Point(1, 0, "AA")
AB = Point(3, 0, "AB")

POINTS = (A, B, C, D, E, F, G, H, I, J, K, L, M, N,
          O, P, Q, R, S, T, U, V, W, X, Y, Z, AA, AB)

VOISINS = {A : (B, C, D, E, F),
           B : (V, C, D, E, G, AA, A),
           C : (W, D, E, L, H, R, AB, B, A),
           D : (X, E, M, I, T, C, B, A),
           E : (J, D, C, B, A),
           F : (A, G, O, H, I, P, J),
           G : (B, V, O, H, I, P, J, AA, F),
           H : (L, C, W, I, P, J, R, AB, O, G, F),
           I : (M, D, X, P, J, T, H, O, G, F),
           J : (E, P, I, H, O, G, F),
           K : (L, M, N, O, Q),
           L : (C, W, M, N, H, R, AB, K),
           M : (D, X, N, I, T, L, K),
           N : (P, U, S, M, L, K),
           O : (K, H, I, P, J, Q, G, F),
           P : (N, J, U, S, I, H, O, G, F),
           Q : (O, K, R, S),
           R : (H, L, C, W, S, AB, Q),
           S : (U, P, N, R, Q),
           T : (I, M, D, X, U, Z),
           U : (P, N, Z, S, T),
           V : (W, B, G, AA),
           W : (C, L, H, R, AB, V),
           X : (Y, D, M, I, T),
           Y : (Z, X),
           Z : (Y, U, T),
           AA : (G, B, V, AB),
           AB : (R, H, L, C, W, AA)}

## Fonctions

def vers_droite(A: Point, B: Point) -> bool:
    return A.y == B.y and A.x < B.x

def vers_gauche(A: Point, B: Point) -> bool:
    return A.y == B.y and A.x > B.x

def vers_haut(A: Point, B: Point) -> bool:
    return A.x == B.x and A.y < B.y

def vers_bas(A: Point, B: Point) -> bool:
    return A.x == B.x and A.y > B.y

def est_rectangle(A: Point, B: Point, C: Point, D: Point) -> bool:
    return (vers_droite(A, B)
        and vers_bas(B, C)
        and vers_gauche(C, D)
        and vers_haut(D, A))

def compte_rectangles():
    l = []
    for A1 in POINTS:
        for A2 in VOISINS[A1]:
            for A3 in VOISINS[A2]:
                for A4 in VOISINS[A3]:
                    if est_rectangle(A1, A2, A3, A4):
                        l.append((A1, A2, A3, A4))
    print(len(l))
    return l