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fermatslibrary's profile
Fermat's Library
Fermat's Library
Fermat's Library
@fermatslibrary

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Fermat's Library

@fermatslibrary

A platform for illuminating academic papers. We publish an annotated paper every week. Our chrome extension for arXiv: https://fermatslibrary.com/librarian 

fermatslibrary.com
Joined September 2015

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    Fermat's Library‏ @fermatslibrary 6 Mar 2019
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    120 is the maximum number of sides a semi-regular dice (all sides the same shape and same area) can have.pic.twitter.com/MdcwI24lq6

    5:29 AM - 6 Mar 2019
    • 679 Retweets
    • 2,650 Likes
    • Kuş open access etc 🤔 Ignacio Montenegro Rojas Manuela Constantinescu Alcoholic Keverage Gustaf Josefson ᚻᛂᛚᚵ ᚸᛞ Leen
    42 replies 679 retweets 2,650 likes
      1. New conversation
      2. Luis Batalha  🇵🇹 🇺🇸‏ @luismbat 6 Mar 2019
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        Replying to @fermatslibrary

        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!

        2 replies 6 retweets 57 likes
      3. Robert (Bob) Bosch‏ @baabbaash 6 Mar 2019
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        Replying to @luismbat @fermatslibrary

        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).

        3 replies 8 retweets 91 likes
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      2. Andrew Wertheim‏ @awertheim 6 Mar 2019
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        Replying to @fermatslibrary

        Why is this the case?

        1 reply 0 retweets 8 likes
      3. ᖇᗝᗷᗴᖇ丅 ᔕᗝᔕᎥᑎ.‏ @ChompyDuchamp 6 Mar 2019
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        Replying to @awertheim @fermatslibrary

        This explains why a bit... essentially I get from this that any more sides and it will roll foreverhttps://youtu.be/516U4whg4GU 

        1 reply 2 retweets 24 likes
      4. 1 more reply
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      2. Rolf‏ @rolfje 6 Mar 2019
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        Replying to @fermatslibrary

        Is that a mathematical limit which is provable, or simply a practical limit?

        1 reply 0 retweets 8 likes
      3. Matthew Skala  😷‏ @mattskala 6 Mar 2019
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        Replying to @rolfje @fermatslibrary

        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.

        1 reply 0 retweets 4 likes
      4. 4 more replies
      1. Durr‏ @ZakFreeThinker 6 Mar 2019
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        Replying to @fermatslibrary

        You know shit's about to go down when you're wondering through a dungeon and the DM pulls one of those out

        2 replies 1 retweet 70 likes
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      1. Robert Fathauer‏ @RobFathauerArt 7 Mar 2019
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        Replying to @fermatslibrary

        Produced by The Dice Lab, and available on their online store: https://mathartfun.com/DiceLabDice.html …

        0 replies 2 retweets 5 likes
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      2. Kalle Leppälä‏ @kalle_leppala 6 Mar 2019
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        Replying to @KKZiomek0 @chaturv3di @fermatslibrary

        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).

        1 reply 0 retweets 1 like
      3. AndruC‏ @AndruC 6 Mar 2019
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        Replying to @kalle_leppala

        If semi-regular polyhedra have regular sides, what distinguishes them from regular polyhedra?

        1 reply 0 retweets 1 like
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