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Great Dirhombicosidodecahedron ("Miller's Monster")

83 points · 22 comments · cobbzilla

  1. skrebbel · · focus · HN ↗
    I don’t understand what this is. Wikipedia says a uniform polyhedron means that all faces are regular. If all faces are regular, that means its edges are all the same length right? And corners the same angles. But if I look at the photo I can’t find a single face that has that property. Am I looking wrong or am I simply misunderstanding what I’m looking at?
    1. PowerElectronix · · focus · HN ↗
      It's a degenerate polyhedron. Their faces intersect and cross one another.
      1. skrebbel · · focus · HN ↗
        Soo it’s not a “real” shape? In the sense that I couldn't mold some clay into this form like I could with eg a football?
        1. gertrunde · · focus · HN ↗
          Given that the article is about making one out of paper, I'd say it is "real".

          Clay might be a difficult material to use to make it though.

          I'd imagine it could probably be made via CNC or 3D printing or similar.

        2. nyankosensei · · focus · HN ↗
          It was made out of paper sheets printed by the “Great Stella” software available elsewhere on the same site:

          <a href="https:&#x2F;&#x2F;www.software3d.com&#x2F;Stella.php" rel="nofollow">https:&#x2F;&#x2F;www.software3d.com&#x2F;Stella.php

    2. ffhh · · focus · HN ↗
      You are assuming that the faces don&#x27;t intersect, and that the faces have edges that don&#x27;t intersect. The easiest example of a polyhedron with self-intersecting behavior to wrap your head around is IMO the small stellated dodecahedron, made from twelve pentagrams.

      If you want to dive in a bit into strange polyhedra, I can really recommend this YouTube video: <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=_hjRvZYkAgA" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=_hjRvZYkAgA

      1. skrebbel · · focus · HN ↗
        Thanks! That &quot;small stellated dodecahedron&quot; drove the point home for me.

        (also TIL a 5-pointed star counts as a regular polygon, feels like cheating somehow)

        1. kadoban · · focus · HN ↗
          &gt; feels like cheating somehow

          Yeah, we&#x27;re used to &quot;convex&quot; polygons. That&#x27;s the phrasing to remove that part that feels wrong.

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