## Are 5 tetrahedra connected by vertices possible in Stella 3d?

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platonic
Posts: 8
Joined: Sun Mar 26, 2023 3:10 pm

### Are 5 tetrahedra connected by vertices possible in Stella 3d?

Hi there.

Is there a way to create in Stella 3d a model of a tetrahedron every vertex of which is a vertex of another tetrahedron?

In other words, 4 tetrahedra connected to a 5th, central tetrahedron?

If so, is there a way to independently label the elements of each tetrahedron in this construction?

Platonic.

robertw
Posts: 676
Joined: Thu Jan 10, 2008 6:47 am
Location: Melbourne, Australia
Contact:

### Re: Are 5 tetrahedra connected by vertices possible in Stella 3d?

First I tried "Poly-> Put Models on Faces/Vertices", choosing the vertex option and applying to all, but you can't easily control orientation with this feature, and it ended up like this:

So I thought of another approach. First, set the edge length to 1 (Scale->Edge Length), and then measure the height of a tetrahedron using measurement mode (enter measurement mode, Shift-click on a vertex, then Shift-click on opposite face).

Go to "Scale->Measured Distance" and copy the value. You can exit measurement mode now.

Now create a triangular prism. Set the edge length to 1.
Go to "Scale->Stretch (Non-Uniform Scale)". Select "Set height to" and paste in the height of a tetrahedron from earlier, then add "* 2" at the end. Yep, it can do inline calculations.

Now we have a triangular prism twice the height of a tetrahedron. If we excavate a tetrahedron from each end, their vertices will touch in the middle.

First, put this prism in a memory slot, we'll need it later (type "m1").

Let's excavate a tetrahedron from just one end: select one of the triangular faces, "Poly->Augment Polyhedron" (or just hit "a"), select the excavate option and "selected face only".

Hit OK and hit Enter to confirm the preview. Select the triangle at the other end, the one that wasn't excavated, and put it in another memory slot (type "m2").

Now go back to a tetrahedron and use Poly->Augment Polyhedron again. Select the second memory slot from the drop-down, and "Excavate" and "All faces of same type".

Hit OK and Enter. You should get this:

Select one of the rectangular (yellow) faces and augment again, this time choosing the first memory slot. Hit OK and Enter again, and prepare for some magic:

platonic
Posts: 8
Joined: Sun Mar 26, 2023 3:10 pm

### Re: Are 5 tetrahedra connected by vertices possible in Stella 3d?

That is magnificent Rob.

Thank you so much for this.

Also a great opportunity for me to learn new features I've never used, and your instructions are really helpful.

Have a great weekend!