Great Dirhombicosidodecahedron ("Miller's Monster")

Re:Great Dirhombicosidodecahedron ("Miller's Monster") by skrebbel on Thursday October 01, 2026 @02:41AM (#49918436)

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?

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Re:Great Dirhombicosidodecahedron ("Miller's Monster") by PowerElectronix on Thursday October 01, 2026 @03:18AM (#49918719)

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

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Re:Great Dirhombicosidodecahedron ("Miller's Monster") by skrebbel on Thursday October 01, 2026 @05:36AM (#49919618)

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?

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Re:Great Dirhombicosidodecahedron ("Miller's Monster") by gertrunde on Thursday October 01, 2026 @08:04AM (#49920570)

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.

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Re:Great Dirhombicosidodecahedron ("Miller's Monster") by nyankosensei on Thursday October 01, 2026 @09:10AM (#49921190)

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

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Re:Great Dirhombicosidodecahedron ("Miller's Monster") by ffhh on Thursday October 01, 2026 @05:57AM (#49919749)

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

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Re:Great Dirhombicosidodecahedron ("Miller's Monster") by skrebbel on Thursday October 01, 2026 @09:44AM (#49921615)

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)

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Re:Great Dirhombicosidodecahedron ("Miller's Monster") by kadoban on Sunday October 04, 2026 @07:29PM (#49959022)

> feels like cheating somehow

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

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