Tetrahedron Troubles

Support Modeling
1

http://www.youtube.com/bareflix#p/u/6/5MJpsACRkDU

I’m trying to create a model of an equilateral tetrahedron. The video above shows one of the ways I’ve tried.
I start with an equilateral triangle and duplicate it.
I rotate the duplicate 60 degrees up on the X axis. So far so good.
Then I duplicate one of the cylinders, rotate it 30 degrees toward the center then 60 degrees up.
That seems like it should work, but as you can see from the end of the video, things don’t line up correctly.
Can anyone explain why this doesn’t work or give any suggestions on what else to try?

I’ve seen examples where a tetrahedron is build with the corners and diagonals of a cube, but that approach won’t work because I need cylinders connecting the points, and the cylinders have to be rotated into position (at least AFAIK).

–
Chris

2

Well, the answer to this question is quite simple, the angle between a face and the opposite side is not 60°.
Wikipedia

To use the described in the video, the first rotation should be about 70.5288° and the last one should be about 54.7356°

3

I was doing this today. I added a cone with three vertexes (actually it has four, Blender can’t count). The crucial part is getting the “Depth” value right (the height of the tetrahedron). The height of a tetrahedron of edge length 1 is 0.81649658; but the bottom edges of the cone default to 1.732, so you have to scale the height up, multiplying by that, meaning the magic depth value is 1.414172 or so.

4

it’s a pain to calculate this in viewport

so i just did a script to do tetrahedron

but not yet release it cause my triangle script is not finish yet !

but i can make a simple script to do this tetradrong alone

anyway PM me if you want it

salutations

5

For info, one of the add-ons that’s included in blender 2.5 (recent builds) is Add Mesh: Regular Solids. This includes adding a tetrahedron as well as many other solids.