Hi folks.
Just in case someone is interested in the Platonic solids (also called Pythagorean solids),
see these two SU file that show the relation between:
1 - The cube or hexahedron (6 square faces) and the octahedron (8 triangular faces).
2 - The dodecahedron (12 pentagonal faces) and the icosahedron (20 triangular faces).
For each pair, you can get from one solide to the other by joining the center of each faces to the center of its neighbors faces.
For the tetrahedron, you will get another smaller tetrahedron if you use this procedure.
In conclusion:
1 - You can get the tetrahedron and the octahedron from a cube (see previous posts).
2 - You can get the icosahedron from three intersecting golden rectangles each at 90° from the others two as was shown in a thread somewhere.
3 - You can get the dodecahedron from an icosahedron.
Thus, you can get all five solids with great precision using only basic SU tools and without using any mathematics.
Just ideas.