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Solved! I'm very curious what the mathematical construction is that you derived this from. I thought you might be referring to the seven color theorem for tori, but that didn't seem to help me find the solution. 

Thanks for making this!

No, it is just this exact problem – aHR0cHM6Ly9lcmljaC1mcmllZG1hbi5naXRodWIuaW8vbWF0aG1hZ2ljLzA5MDMuaHRtbA==