dPowBalancer.py

from math import factorial
from sympy.utilities.iterables import multiset_permutations

print("Searching...")

# Numerically balanced dice
# To calculate:
# 1. Find the average value of a face
# 2. Multiply that average by the number of faces touching a vert.
#    The result is the value each vert should have.
# 3. The d30 has 2 types of verts. Face averages come to a ##.5 value, so
#    normally some vertices have to be higher and others lower than that.

# For a d30 that uses: [0,1,1,2,2,2,3,3,3,3,4,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9]
# Average face value: 4.5
# 32 verts total. 20 with 3-faces. 12 with 5-faces.
# 3-faces need 13.5 -- Thats 10x 13s and 10x 14s
# 5-faces need 22.5 -- Thats 6x 22s and 6x 23s

# We will use the following mappings.
# Negatives used for "inverse" side. Vertices labeled with their desired sums.
#                  -4 E_-"\ 23 /`-_F -2
#                   _-"    \  /    `-_
#    -4             \   11  \/   9   /
#      D_-``-_       \    _-``-_    /       _-``-_A -2
#  22_-"  12  `-_     \_-"      `-_/     _-"  8   `-_ 22
#-7 /`-_      _-"\  22/`-_  10  _-"\23  /`-_      _-"
# C/    `-__-"    \  /    `-__-"    \  /    `-__-"B -14
# /  14   /\   13  \/  0    /\   6   \/  7    /
# `-_    /  \    _-"`-_    /  \    _-"`-_    /C -14
#   B`-_/    \_-"  1   `-_/    \_-"  5   `-_/
#  -8      23/`-_      _-"\22   `-_      _-"\23
#       -8 A/    `-__-"    \       `-__-"    \D -12
#          /   2   /\   3   \         \   4   \
#          `-_    /  \    _-"          \    _-"
#         -9 F`-_/    \_-"    22        \_-"E -11
triplets = [ [11,12,-4], [9,10,11], [8,9,-2], [12,13,14], [0,1,13], [0,6,10], [5,6,7], [7,8,-14], [1,2,3], [3,4,5] ]
pentlets = [ [0,10,11,12,13], [6,7,8,9,10], [0,1,3,5,6], [4,5,7,-12,-14], [1,2,13,14,-8], [2,3,4,-9,-11] ]
pentsums = [       22,            23,           22,           23,              23,              22      ]

# Permute half of the die values, skipping the first, as thats always 0. We will permute inverting them later.
face_bag = [1,1,2,2,2,3,3,3,3,4,4,4,4,4] #len 14
flip_bag = [0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1]
count = 0
try:
    for raw_face_perm in multiset_permutations(face_bag):
        # Pumutations of flipping bits
        for flip_perm in multiset_permutations(flip_bag,14):
            count += 1
            face_perm = [0, *raw_face_perm]
            # Flip the same spots as the bits
            for i in range(len(flip_perm)):
                if flip_perm[i]: face_perm[i+1] = 9 - face_perm[i+1]
            # Should sum 13 or 14
            n13 = 0
            n14 = 0
            fail = False
            for trips in triplets:
                sum = 0
                for t_face in trips:
                    sum += face_perm[t_face] if t_face >= 0 else 9 - face_perm[abs(t_face)]
                if sum == 13: n13 += 1
                elif sum == 14: n14 += 1
                else:
                    fail = True
                    break

                if n13 > 10 or n14 > 10:
                    fail = True
                    break
            if fail: continue

            fail = False
            for (pent_i, pents) in enumerate(pentlets):
                sum = 0
                for p_face in pents:
                    sum += face_perm[p_face] if p_face >= 0 else 9 - face_perm[abs(p_face)]
                if sum != pentsums[pent_i]:
                    fail = True
                    break
            if fail: continue

            print( "Found %s" %[face_perm] )
except KeyboardInterrupt:
    print("Interrupt")
expected = (factorial(14) / (factorial(2)*factorial(3)*factorial(4)*factorial(5))) * (factorial(14)/(factorial(8)*factorial(8)))
print( "Got to %s\n    of %s\n    (%s %%)" %(count, expected, (count/expected*100)) )

# Full die unwrap diagram
#     _-"\              _-"\              _-"\              _-"\              _-"\
#  _-"    \          _-"    \          _-"    \          _-"    \          _-"    \
#  \       \         \       \         \       \         \       \         \       \
#   \    _-"`-_       \    _-"`-_       \    _-"`-_       \    _-"`-_       \    _-"`-_
#    \_-"      `-_     \_-"      `-_     \_-"      `-_     \_-"      `-_     \_-"      `-_
#    /`-_      _-"\    /`-_      _-"\    /`-_      _-"\    /`-_      _-"\    /`-_      _-"\
#   /    `-__-"    \  /    `-__-"    \  /    `-__-"    \  /    `-__-"    \  /    `-__-"    \
#  /       /\       \/       /\       \/       /\       \/       /\       \/       /\       \
#  `-_    /  \    _-"`-_    /  \    _-"`-_    /  \    _-"`-_    /  \    _-"`-_    /  \    _-"`-_
#     `-_/    \_-"      `-_/    \_-"      `-_/    \_-"      `-_/    \_-"      `-_/    \_-"      `-_
#             /`-_      _-"     /`-_      _-"     /`-_      _-"     /`-_      _-"     /`-_      _-"
#            /    `-__-"       /    `-__-"       /    `-__-"       /    `-__-"       /    `-__-"
#           /       /         /       /         /       /         /       /         /       /
#           `-_    /          `-_    /          `-_    /          `-_    /          `-_    /
#              `-_/              `-_/              `-_/              `-_/              `-_/

# Discovered results
#[0,  8, 1, 4,  6,  3, 7, 4,  3,  2, 7, 5,  5, 5, 3]
#[0,  8, 1, 5,  5,  3, 6, 5,  2,  3, 7, 4,  6, 5, 2]
#[0,  8, 2, 3,  6,  4, 7, 3,  5,  1, 7, 6,  4, 5, 4] This one looks promising
#                     E_-"\ 23 /`-_F
#                   _-"    \  /    `-_
#                   \   6   \/   1   /
#      D_-13-_       \    _-14-_    /       _-13-_A
#  22_-"   4  `-_     \_-"      `-_/     _-"  5   `-_ 22
#   /`-_      _-"\  22/`-_   7  _-"\23  /`-_      _-"
# C/    `-13-"    \  /    `-14-"    \  /    `-13-"B
# /   4   /\   5   \/  0    /\   7   \/  3    /
# `-_    /  \    _-13-_    /  \    _-14-_    /C
#   B`-_/    \_-"  8   `-_/    \_-"  4   `-_/
#   4      23/`-_      _-"\22   `-_      _-"\23
#          A/    `-13-"    \       `-13-"    \D
#          /   2   /\   3   \         \   6   \
#        14`-_    /  \    _-"          \    _-"
#            F`-_/    \_-"    22        \_-"E

#[0, 8, 3, 2, 5, 6, 6, 2, 5, 2, 8, 4, 5, 5, 3]