import math
import itertools

def parse_obj_file(file_path):
    vertices = []
    with open(file_path, 'r') as file:
        for line in file:
            if line.startswith('v '):
                parts = line.split()
                vertices.append((float(parts[1]), float(parts[2]), float(parts[3])))
    return vertices

def calculate_bounding_box(file_path):
    vertices = parse_obj_file(file_path)

    min_x = min_y = min_z = float('inf')
    max_x = max_y = max_z = float('-inf')

    for x, y, z in vertices:
        min_x, max_x = min(min_x, x), max(max_x, x)
        min_y, max_y = min(min_y, y), max(max_y, y)
        min_z, max_z = min(min_z, z), max(max_z, z)

    delta_max = max(max_x - min_x, max_y - min_y, max_z - min_z)
    center = [(max_x + min_x) / 2, (max_y + min_y) / 2, (max_z + min_z) / 2]

    factor = 2.5 / math.sqrt(2)

    coords = []
    for i, j, k in itertools.product([-1, 1], repeat=3):
        x = center[0] + i * delta_max * factor
        y = center[2] + j * delta_max * factor
        z = center[1] + k * delta_max * 2.5
        coords.append((x, y, z))
    return coords