Trying to create a tetrahedron

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#1

Hi,

Online tips & tutorials haven’t helped me out with this problem so-far. I’m trying to figure out how to draw a tetrahedron, or pyramid with triangular base; the first of the platonic solids. I got as far as creating a single equilateral triangle as a base, but I’m not sure how I would then go from this into a pyramid shape. I tried extruding it upwards and then trimming a rotated rectangular piece off of it, but this doesn’t result in perfectly equilateral geometry.

Any help would be appreciated.

Thanks

Why there is a broken hole in the mesh?
#2

To easily do this, you’d need a surface modeling tool I think.

You can do it in Shapr3D as well, but you’ll need to apply some math and brute force. :smiley:

It took me about 5 minutes to create this one.

Tetrahedron:

These are the shapes (big cubes) I used to subtract with (tetrahedron is in the middle). You have to rotate these cubes by 120 degrees around one axis and by 19.4712 degrees or something close to this (have to check the math to be sure) on the other axis. Align the big blocks on the same triangle, and subtract.

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#3

Ok, this is the solution I was thinking of but I kept getting the angle wrong. Thanks!

#4

To be exact with the math:

First, you need to know the dihedral angle of the tetrahedron.

That is beta on the picture. It is calculated as arccos(1/3) which is 70.528779°.

So you want to rotate with 90° - 70.528779° which is 19.471221°. So you should rotate with 19.47° I think to get the perfect shape.

If you want to, I can do a tutorial video how I did it.

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#5

Please do! It would be nice :slightly_smiling_face:

#6

Here’s the workflow:

  • draw a triangle
  • extrude it
  • extrude all sides with the create “new” shape command
  • rotate each cube on the base side of the triangle with 90-arccos(1/3) so 19.471221°
  • subtract the 3 cubes from the triangular shape (note: the sketch layer needs to be hidden so you can select the shape in the middle)
  • voila, there’s your tetrahedron

Here’s a quick video:

(this version of the app will be released in a few days, so some buttons might look a little different, but you can do the exact same thing in Shapr3D v2.0.6 which is available in the App Store)

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#7

Thank you, appreciated :+1:t2:

1 Like