Исходно:

x = (-1)^(k+1) pi/12 + pi/4 + pi n + pi k/2
y = (-1)^(k+1) pi/12 - pi/4 - pi n + pi k/2

x = (-1)^(k) pi/12 + pi/4 - pi n + pi k/2
y = (-1)^(k) pi/12 - pi/4 + pi n + pi k/2

1) k = 2m, k = 2m+1

x = -pi/12 + pi/4 + pi n + pi m
y = -pi/12 - pi/4 - pi n + pi m

x = pi/12 + pi/4 - pi n + pi m
y = pi/12 - pi/4 + pi n + pi m

x = pi/12 + pi/4 + pi n + pi m + pi/2
y = pi/12 - pi/4 - pi n + pi m + pi/2

x = -pi/12 + pi/4 - pi n + pi m + pi/2
y = -pi/12 - pi/4 + pi n + pi m + pi/2

2) mod 24

x / (pi/12) = -1 + 3 + 12 n + 12 m
y / (pi/12) = -1 - 3 - 12 n + 12 m

x / (pi/12) = 1 + 3 - 12 n + 12 m
y / (pi/12) = 1 - 3 + 12 n + 12 m

x / (pi/12) = 1 + 3 + 12 n + 12 m + 6
y / (pi/12) = 1 - 3 - 12 n + 12 m + 6

x / (pi/12) = -1 + 3 - 12 n + 12 m + 6
y / (pi/12) = -1 - 3 + 12 n + 12 m + 6

3)

x / (pi/12) = 2 + 12 n + 12 m
y / (pi/12) = -4 - 12 n + 12 m

x / (pi/12) = 4 - 12 n + 12 m
y / (pi/12) = -2 + 12 n + 12 m

x / (pi/12) = 10 + 12 n + 12 m
y / (pi/12) = 4 - 12 n + 12 m

x / (pi/12) = 8 - 12 n + 12 m
y / (pi/12) = 2 + 12 n + 12 m

4)

x / (pi/12) = 2 + 12 (n+m)
y / (pi/12) = -4 - 12 (n-m)

x / (pi/12) = 4 - 12 (n-m)
y / (pi/12) = -2 + 12 (n+m)

x / (pi/12) = 10 + 12 (n+m)
y / (pi/12) = 4 - 12 (n-m)

x / (pi/12) = 8 - 12 (n-m)
y / (pi/12) = 2 + 12 (n+m)

5)


x / (pi/12) = 2 + 12 (n+m)
y / (pi/12) = -4 - 12 (n-m)

x / (pi/12) = 4 - 12 (n-m)
y / (pi/12) = -2 + 12 (n+m)

x / (pi/12) = 10 + 12 (n+m)
y / (pi/12) = 4 - 12 (n-m)

x / (pi/12) = 8 - 12 (n-m)
y / (pi/12) = 2 + 12 (n+m)