What is this Polyhedra called.

For general discussion of polyhedra, not necessarily Stella-specific.
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eligius1427
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What is this Polyhedra called.

Post by eligius1427 » Sun Oct 17, 2021 10:15 pm

Hello, I found this toy and am curious what geometric form it is called. It is essentially 6 5-pointed stars interwoven. At first I thought it was a dodecahedron, but after closer inspection it seems to have some triangle shapes in it as well.


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eligius1427
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Re: What is this Polyhedra called.

Post by eligius1427 » Sun Oct 17, 2021 10:25 pm

is it possibly a variation of an Icosidodecahedron?

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robertw
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Re: What is this Polyhedra called.

Post by robertw » Mon Oct 18, 2021 1:34 am

eligius1427 wrote:
Sun Oct 17, 2021 10:15 pm
Hello, I found this toy and am curious what geometric form it is called. It is essentially 6 5-pointed stars interwoven. At first I thought it was a dodecahedron, but after closer inspection it seems to have some triangle shapes in it as well.
Yeah I've seen these before. It's not really a polyhedron itself, but it's close to a few.

Just looking at it, it's most reminiscent of the compound of 5 tetrahedra: https://www.software3d.com/5Tet.php
Image

But this one is really a compound of 6 pentagonal or pentagrammatic prisms. Stella has both of these in its library too, but they look different at first because the prisms have square sides, making them much thicker than the pieces in your toy.

Compound of 6 pentagonal prisms:
Image

Squashing each one down to 0.15 of its original height looks a bit more like it:
Image

Compound of 6 pentagrammatic prisms:
Image

And after squashing each one down to 0.0618 of their original heights (I went for roughly the golden ratio).
Image

The pieces in the toy are somewhere between pentagons and pentagrams, so you could make something intermediate to get closer.

eligius1427
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Re: What is this Polyhedra called.

Post by eligius1427 » Mon Oct 18, 2021 12:39 pm

Thank you!

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robertw
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Re: What is this Polyhedra called.

Post by robertw » Mon Oct 18, 2021 1:42 pm

That's OK. I forgot to mention another model I made that probably looks even more like it. A stellation of the small stellated truncated dodecahedron.
https://www.software3d.com/StelSSTD.php
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Ulrich
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Re: What is this Polyhedra called.

Post by Ulrich » Tue Oct 19, 2021 9:13 am

I tried to make something like that from 6 „pentagrammic rings“

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Ulrich

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robertw
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Re: What is this Polyhedra called.

Post by robertw » Tue Oct 19, 2021 1:26 pm

Ulrich wrote:
Tue Oct 19, 2021 9:13 am
I tried to make something like that from 6 „pentagrammic rings“
Nice job

eligius1427
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Re: What is this Polyhedra called.

Post by eligius1427 » Sun Oct 31, 2021 3:33 pm

Ulrich wrote:
Tue Oct 19, 2021 9:13 am
I tried to make something like that from 6 „pentagrammic rings“

Image

Ulrich
That looks very much like the toy!

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