31.03.2020 | Polyhedrons inside Polyhedrons

This lesson consisted of using the polyhedrons created in the previous class and fitting them inside each other.

In geometry, any polyhedron is associated with a second dual figure, where the vertices of one correspond to the faces of the other.

The dual polyhedron of the tetrahedron is also a tetrahedron since it is a self-dual polyhedron.

First, a triangle is placed inside the tetrahedron, making sure its vertices are aligned with the tetrahedron faces.

A copy of the tetrahedron solid is scaled and mirrored using Scale and 3D Mirror commands. This makes it possible for a smaller tetrahedron in the right position to fit inside the original one.

After this, it is a matter of aligning this small tetrahedron with the triangle inside of the large one, using the Align command.

The cube is a dual polyhedron to the octahedron.

Instead of drawing a triangle inside, a square is drawn.

The octahedron is scaled and aligned with the square drawn inside of the cube. 

This process can be repeated non-stop.
An example of this is another cube fitted inside of the octrahedron, now placed inside of the original cube.

The final dual polyhedrons were the icosahedron which fits into the dodecahedron. 

The process repeats itself only adjusting the forms. In this case a pentagon.