a simple script to calculate cube states

cube_state.py

#!/usr/bin/env python
from math import factorial
from sys import argv

F4 = factorial(4) # 4 same-look centerpieces
F8 = factorial(8) # 8 corners
F12 = factorial(12) # 12 midges
F24 = factorial(24) # 24 wings/centers

P3_8 = 3 ** 8 # corner twists
P2_12 = 2 ** 12 # midge flips


CORNER_STATES = P3_8 * F8
MIDGE_STATES = P2_12 * F12
CENTER_STATES_PER_GROUP = F24 // (F4 ** 6)
WING_STATES_PER_GROUP = F24

def calc(n):
	even = (n % 2 == 0)
	centerGroupCount = ((n - 2) ** 2) // 4
	wingGroupCount = (n - 2) // 2
	states = (
		# centers
		CENTER_STATES_PER_GROUP ** centerGroupCount
		# wings
		* WING_STATES_PER_GROUP ** wingGroupCount
		# corners
		* CORNER_STATES
		# midges if exists
		* (1 if even else MIDGE_STATES)
		# 24 orientations * 3 corner twists for even-order cubes
		# 2 midge flips * 3 corner twists * 2 permutations for odd-order cubes
		// (72 if even else 12))
	return states

class OrderError(Exception):
	pass

def main():
	MIN_ORDER = 2
	MAX_ORDER = 200
	try:
		order = int(argv[1])
		if order < MIN_ORDER or order > MAX_ORDER:
			raise OrderError('Order should between {} and {}'.format(MIN_ORDER, MAX_ORDER))
	except OrderError as e:
		print(e)
		return
	except ValueError as e:
		print('Wrong order: ' + argv[1])
		return
	except:
		print('Usage: python {} cube_order'.format(__file__))
		return
	print(calc(order))

if __name__ == '__main__':
	main()