def make_grid(freq, m, n):
    """Make the geodesic pattern grid"""
    grid = {}
    rng = 2 * freq // (m + n)
    for i in range(rng):
        for j in range(rng):
            x = i * -n + j * (m + n)
            y = i * (m + n) + j * -m
            if x >= 0 and y >= 0 and x + y <= freq:
                grid[i, j] = x, y
    return grid
