I am right now writing a story about a world full of twisty puzzles where it starts out like a city with 3 friendship networks and becomes 3 empires with 1 being the cubes, 1 being the cuboids, and 1 being the other shapes which include dodecahedra and pentahedra and tetrahedra and lots of others. In my story for both the cubes and cuboids the maximum dimension for any side is 17 and minimum is 1. For the other shapes it is similar but with their equivalents. For the dodecahedra they follow the metric prefixes. 3x3: megaminx 5x5: gigaminx 7x7: teraminx 9x9: petaminx 11x11: examinx 13x13: zettaminx 15x15: Yottaminx 17x17: Kiloyottaminx(following the double prefix rules of smaller before larger kiloyotta- means 1000 * yotta) If something new is cooked or discovered there is a rotation of jobs in the empire of cubes. It started like this: Gardener: 17x17 Animal care: 16x16 Meteorologist: 1x1 Scientist: 6x6 Teacher: 5x5 Cook: 7x7 Accountant: 2x2 Angler: 8x8 Doctor: 9x9 Guard (1st degree): 10x10 Guard (2nd degree): 11x11 Guard (3rd degree): 12x12 Guard (4th degree): 13x13 Guard (5th degree): 14x14 Guard (6th degree): 15x15 The 3x3 is always the emperor As for determining the cube that will take the job after a rotation here is the math: If N > 17 then N+1 If N = 17 then 1x1 Here is how it was after the first batch of cheddar cheese was made: Gardener: 1x1 Animal care: 17x17 Meteorologist: 2x2 Scientist: 6x6 Teacher: 5x5 Cook: 7x7 Accountant: 4x4 Angler: 9x9 Doctor: 10x10 Guard (1st degree): 11x11 Guard (2nd degree): 12x12 Guard (3rd degree): 13x13 Guard (4th degree): 14x14 Guard (5th degree): 15x15 Guard (6th degree): 16x16 And here is how it is now after the pizza was made: Gardener: 2x2 Animal care: 1x1 Meteorologist: 4x4 Scientist: 7x7 Teacher: 6x6 Cook: 8x8 Accountant: 5x5 Angler: 10x10 Doctor: 11x11 Guard (1st degree): 12x12 Guard (2nd degree): 13x13 Guard (3rd degree): 14x14 Guard (4th degree): 15x15 Guard (5th degree): 16x16 Guard (6th degree): 17x17 The cubes have genes that determine what cubes they will get given a cube they are mating with and external factors like temperature and sterility as in no viruses and no bacteria or other infectious agents. The determination of what it should be is larger cube - smaller cube so that 3x3 - 2x2 = 1x1 etc. If they are in the cold it is the larger of the middle values between the larger cube and the smaller cube and high water gives lower of the middle values. High food gives the sum meaning that a 17x17 mating with a 16x16 and eating a lot of food will give birth to a 33x33 cube. In any case where there was a high food condition surgery needs to be done. If they are in a sterile environment they stay as little 1x1s proving that immunity, not sterility is needed. In a hot environment the baby dies during the pregnancy and is never born. These cubes are special in that if 1 or more pieces come off the cube that area of the cube is automatically cauterized so that there is little or no bleeding. This is nice.