Add Truncated Trapezohedra

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Julius
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Joined: Sun Jun 18, 2023 1:25 am

Add Truncated Trapezohedra

Post by Julius » Sun Jun 18, 2023 2:55 am

Hello.
I've purchased Stella4D 1 year ago.
I want to request the addition of the Truncated Trapezohedra. All with regular faces.
These polyhedra appears here: https://en.wikipedia.org/wiki/Truncated_trapezohedron
It would be nice that these polyhedra appear on Stella4D and Great Stella.
The polyhedra list could be:
Truncated Triangular Trapezohedron
Truncated Square Trapezohedron
The Truncated Pentagonal Trapezohedron probably don't because is the same as the Dodecahedron.
Truncated Hexagonal Trapezohedron
Truncated Heptagonal Trapezohedron
Truncated Octagonal Trapezohedron
Truncated Decagonal Trapezohedron
Truncated N-gonal Trapezohedron
When I was a kid I had the trial version of Poly from Pedagoguery Software and I had Great Stella DEMO too.
I discovered that:
The Tetrahedron is a Triangular Pyramid
The Hexahedron or Cube is a Square Prism
The Octahedron is a Square Dipyramid
The Icosahedron is a Gyroelongated Pentagonal Dipyramid
And I asked myself a question:
What is the Dodecahedron?
1 year later I discovered on Wikipedia that this set of polyhedra is named Truncated Trapezohedra. :D
That set are my favorite polyhedra, these are misterious polyhedra because they don't appear anywhere, I only found them on Wikipedia.
Well, that's all, have a nice day.

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robertw
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Re: Add Truncated Trapezohedra

Post by robertw » Sun Jun 18, 2023 3:41 am

I like to think of the octahedron as a triangular antiprism.

It's not too hard to make the polyhedra you want in Stella. It's a bit arbitrary though as to how truncated the points are.

Start with an antiprism, eg a square antiprism if you want to make a truncated square trapezohedron.

You'll notice that the dual is the trapezohedron before truncation.

Image

Change one of the views to the morphing by truncation view, then use Ctrl+Left-drag (move mouse while holding left button) to adjust the amount of truncation. You can choose to truncate a little or a lot, as long as the other vertices don't start getting truncated. Then click the left-and-down button in the top right corner of that view to make it the new base model.

Image

Or with 13-gons:

Image

Only the triangular one needs some additional work, as the antiprism we start with is the regular octahedron, and its dual the cube, so the truncation step will always truncates all the vertices at once. The trick is to squash the octahedron first along the 3-fold axis using "Scale->Stretch (Non-Uniform Scale)".

Image

Julius
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Joined: Sun Jun 18, 2023 1:25 am

Re: Add Truncated Trapezohedra

Post by Julius » Sun Jun 18, 2023 7:48 pm

I've already done that. Thanks for the triangular, I didn't know how to make it.
With this procedure there's no regular pentagons, only the bases are regular.
Is there a way to make it so that regular pentagons appear?

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Ulrich
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Re: Add Truncated Trapezohedra

Post by Ulrich » Mon Jun 19, 2023 5:33 am

No, that can‘t be done. I tried it some years ago, using the function „try to make faces regular“ and it failed.

Ulrich

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robertw
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Re: Add Truncated Trapezohedra

Post by robertw » Mon Jun 19, 2023 1:08 pm

It's not possible to make the pentagons regular. If it was you would have discovered new Johson solids. But the top and bottom polygons are regular.

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