A Near-Miss to the Johnson Solids, Which I’m Naming the Ditrated Dodecahedron, Part Two

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(If you haven’t yet read part one, I strongly recommend reading it first.)

With the help of Tadeusz Dorozinski and Hunter Hughes, my new near-miss (the discovery of which was described here) is now better-understood. The isosceles triangles’ shared bases are about 5% longer than the solid’s other edges, which is within the range generally allowed for near-misses. I have not yet found any mention of this discovery before I found it yesterday, while playing with a broken, plastic d12.

Here is a net for this solid:

Also, here is its dual, as well as a net for the dual.

These images were generated using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.

[Update: I am now convinced that I am not the first person to find this near-miss. On the other hand, I don’t know who that first person actually is.]

4 thoughts on “A Near-Miss to the Johnson Solids, Which I’m Naming the Ditrated Dodecahedron, Part Two”

  1. Pingback: A Near-Miss to the Johnson Solids, Which I’m Naming the Ditrated Dodecahedron, Part One | RobertLovesPi.net

  2. Hello Robert, I have found about this solid quite some time before (at least 2021) but I expect other people to have found it before me, the shape is too simple.
    By replacing the pentagons with pentagonal pyramids pointing inwards you can make it so that all edges are unit length.
    Here is the model on my website
    https://asliceofcuriosity.fr/blog/extra/polyhedra-viewer-geometry12.html?index=663

    I also have a shape solver like Stella in case you need to find other near miss solids:
    https://asliceofcuriosity.fr/assets/polyhedron-form/index-spring-model.html

    Also, I would like to suggest to work together to integrate a 3D viewer for your models into your webpages instead of having a Stella created GIF.
    Let me know what you think : wagyxxygaw@gmail.com

    You also talk about a facebook group about near miss solid, have I missed the link ?

    Best regards,

    Wagyx

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