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# The Bilinski Dodecahedron is a Space-Filling (Tessellating) Polyhedron

I thought I had discovered an obscure polyhedron was space-filling. Turns out it was already known.
 (+5) [vote for, against]

A Bilinski dodecahedron is a polyhedron with 12 faces; each face is a golden rhombus. Although a rhombic dodecahedron also has 12 golden rhombus faces, a Bilinski dodecahedron looks quite different.

Anyway, I thought I was the first to notice that a Bilinski dodecahedron is space-filling. This is because it was not mentioned in readily available information (e.g. wikipedia or mathworld). So I wrote a paper with this discovery. However, it turns out that it was known in a journal article (which has paywall restrictions, hence why I was not originally unaware).

So I tried to edit wikipedia with this information (successfully on one page but unsuccessful on another (and I couldn't be bothered getting into a argument with that editor)).

Anyway, here's the paper if anyone is interested.

 — xaviergisz, May 07 2021

The Bilinski Dodecahedron is a Space-Filling (Tessellating) Polyhedron https://vixra.org/abs/2105.0028
[xaviergisz, May 07 2021]

Bilinski dodecahedron https://en.wikipedi...linski_dodecahedron
[xaviergisz, May 07 2021]

My paper published in Parabola https://www.parabol...ellating-polyhedron
[xaviergisz, Dec 27 2021]

 1. Congratulations on making the discovery independently.

 2. Commiserations that someone else beat you to it.

 3. Don't worry, you're already world famous on this site.

[+]
 — pertinax, May 07 2021

 I am going to say something that I don't understand the meaning of, but sounds like the right thing to say:

 Can this result be generalized to higher dimensions?

Actually, I would like to see a Wikipedia that used "space-filling" principles to organize comments to allow anyone to share their knowledge on any topic and then allow visitors to browse results that are too interesting for the normal mods (who can send comments out of that mod's space into an alternate space)
 — sninctown, May 07 2021

Lego® should come in a number of 'flavours', each based around a different kind of tessellating polyhedron
 — hippo, May 07 2021

Post that as its own idea, [hippo].
 — pertinax, May 07 2021

I wonder if this geometry would make an interesting jewel. Probably not enough, correctly angled, internal reflective surfaces, I guess.
 — wjt, May 08 2021

 [annotate]

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