How to Construct a Tetrahedron in Blender
This tutorial requires basic knowledge of Blender.
Background
Blender’s three-dimensional rectilinear grid allows for easy creation of cube-based objects. But what do you do if you want to create a tetrahedron, a regular polyhedron with four equilateral triangle faces? My initial attempts at this involved trying to create one face on the X-Y plane and rotating a copy up. This turned out to be a lot more trouble than it’s worth because you have to deal with some very specific angles.
After playing with a magnetic toy in the shape of a tetrahedron I realized that it could be inscribed neatly in a cube, with each of its vertexes in a corner of the cube, and each of its edges running along the diagonal of one of the cube’s faces.
In short the coordinates for the vertices of a tetrahedron are:
(+1, +1, +1)
(−1, −1, +1)
(−1, +1, −1)
(+1, −1, −1)
Constructing the Tetrahedron
Create a cube, switch to vertex select mode and rotate the scene so that you can see and select any of its vertices. The image below already has a tetrahedron inscribed in it which should help you locate the new faces you will add. Each vertex of the cube is labeled “A” to “H”:
Select A, D, F. Press [F] to create a face.
Select D, F, G. Press [F] to create a face.
Select A, F, G. Press [F] to create a face.
You now have a tetrahedron inscribed inside the original cube. Let’s cut away the cube:
Select B, C, H & E. Delete these vertices.
You are now left with a tetrahedron:
