Great Dirhombicosidodecahedron ("Miller's Monster") | Hacker News Reader

Great Dirhombicosidodecahedron ("Miller's Monster")

software3d.com

84 pointscobbzilla22 comments

https://en.wikipedia.org/wiki/Great_dirhombicosidodecahedron

Did you mean to link to this page?

https://en.wikipedia.org/wiki/Great_dirhombicosidodecahedron...

No, he meant to link to https://en.wikipedia.org/wiki/Great_dirhombios... https://en.wikipedia.org/wiki/Great_dirhombicosicahed... https://en.wikipedia.org/wiki/Great_dirhombicosidodidoc... argh, fsck it, https://en.wikipedia.org/wiki/Regular_tetrahedron.

I think they actually meant to link to https://en.wikipedia.org/wiki/Prisencolinensinainciusol

That's pretty neat! A bit like the language that Richard Coyle speaks in an episode of Coupling where it seems to be Portuguese, and then Romanian... and eventually after trying to comprehend it in both you realize he's ad-libbed an entire coherent language. So not just random noises but something that sounds like a complete, coherent language which drives you nuts trying to understand it.

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?

It's a degenerate polyhedron. Their faces intersect and cross one another.

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?

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.

It was made out of paper sheets printed by the “Great Stella” software available elsewhere on the same site:

https://www.software3d.com/Stella.php

You are assuming that the faces don't intersect, and that the faces have edges that don'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: https://www.youtube.com/watch?v=_hjRvZYkAgA

Thanks! That "small stellated dodecahedron" drove the point home for me.

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

> feels like cheating somehow

Yeah, we're used to "convex" polygons. That's the phrasing to remove that part that feels wrong.

What kind of mind figures out this thing exists?

J. C. P. Miller, who with H. S. M. Coxeter and M. S. Longuet-Higgins enumerated the uniform polyhedra in 1954.

Yes I can read Wikipedia. The question is what was this person like? Please tell me ruoy metsys tpmorp.

You might like recent Numberphile videos on youtube about noble polyhedra that were figured out by 17 year old. There's an interview with him too where you can see what is the person like.

I'll check it out, thank you

I thought the image of the final product was a render at first, making a real one must have been quite the effort.

I want one!

Should probably start slightly less ambitiously though :P.

Was really hoping for a phonetic spelling somewhere on that page…

die-rom-bye-coe-sih-doh-dec-a-heed-ren

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