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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.
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]
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Annotation:
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1. Congratulations on making the discovery independently. |
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2. Commiserations that someone else beat you to it. |
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3. Don't worry, you're already world famous on this site. |
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I am going to say something that I don't understand the
meaning of, but sounds like the right thing to say: |
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Can this result be generalized to higher dimensions? |
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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) |
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Lego® should come in a number of 'flavours', each based
around a different kind of tessellating polyhedron |
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Post that as its own idea, [hippo]. |
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I wonder if this geometry would make an interesting jewel. Probably not enough, correctly angled, internal reflective surfaces, I guess. |
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