Even though this was first described by Eugène Catalan in 1865 it was only in 2016 that Robert Bosch was able to create the D120. It took almost 2 months of running various accelerated brute-force computations to find out the final shape!
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I didn't create the shape, but I did do the numbering. This d120 is numerically balanced. The numbers on opposite faces sum to 121. And all vertex sums are what they should be (4*60.5 = 242 for degree 4; 6*60.5 = 363; 10*60.5 = 605 for degree 10).
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Why is this the case?
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This explains why a bit... essentially I get from this that any more sides and it will roll foreverhttps://youtu.be/516U4whg4GU
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Is that a mathematical limit which is provable, or simply a practical limit?
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I'm not sure I can recite the proof off the top of my head in 280 characters, but it is provable. Follows from the Euler characteristic; the numbers of edges, vertices, and faces on a polyhedron must meet certain conditions, and "fair die" restricts these numbers too.
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You know shit's about to go down when you're wondering through a dungeon and the DM pulls one of those out
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Produced by The Dice Lab, and available on their online store: https://mathartfun.com/DiceLabDice.html …
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Isohedral means the sides are the same shape, and positioned symmetrically so that the die is fair (symmetry group having only one orbit or something). Semi-regular polyhedra has regular sides, these diamond shapes are not regular (not all angles are the same, i. e. 90 degrees).
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If semi-regular polyhedra have regular sides, what distinguishes them from regular polyhedra?
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