## What is this Polyhedra called.

For general discussion of polyhedra, not necessarily Stella-specific.
eligius1427
Posts: 8
Joined: Sun Oct 25, 2020 6:12 pm

### What is this Polyhedra called.

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.

eligius1427
Posts: 8
Joined: Sun Oct 25, 2020 6:12 pm

### Re: What is this Polyhedra called.

is it possibly a variation of an Icosidodecahedron?

robertw
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Location: Melbourne, Australia
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### Re: What is this Polyhedra called.

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

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:

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

Compound of 6 pentagrammatic prisms:

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

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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Joined: Sun Oct 25, 2020 6:12 pm

### Re: What is this Polyhedra called.

Thank you!

robertw
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### Re: What is this Polyhedra called.

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

Ulrich
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### Re: What is this Polyhedra called.

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

Ulrich

robertw
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### Re: What is this Polyhedra called.

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

eligius1427
Posts: 8
Joined: Sun Oct 25, 2020 6:12 pm

### Re: What is this Polyhedra called.

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

Ulrich
That looks very much like the toy!