# From a tetrahedron to an octahedron

How to transform a tetrahedron into an octahedron: we make some successive sections with 4 planes that round off the vertices and are perpendicular to the rotations axes that go through the 4 couples of vertices (during the construction we get also a uniform polyhedron of type (3,6,6)). The dimensions of the polyhedra in the figure don't reproduce exactly this construction. Instead, the polyhedra in the figure represent the sections of a hypercube with 3-dimensional spaces perpendicular to a diagonal of the hypercube. In the same way, if we section a cube with planes perpendicular to a diagonal, we get triangles and hexagons.

© matematita

immagine di Gian Marco Todesco

The image belongs to the sections...:

Other costructions (3D geometry)

Uniform polyhedra and their duals (3D geometry)

Sections of a hypercube (4D geometry)

Further information:

http://www.toonz.com/personal/todesco