Mathematical Experiment 6

Construct six disks of the same size each touching the other four.

Construct four disks of the same size each touching the other three.

Construct eight spheres of the same size each touching the other three.

Construct four spheres of the same size each touching the other three.

Construct six spheres of the same size each touching the other four.

Construct twelve spheres of the same size each touching the other five.

Construct twenty spheres of the same size each touching the other three.

Construct the hyperboloid of one sheet:

Color the two halves of the hyperboloid of one sheet as thus:

Combining one half of the hyperboloid of one sheet with its reflection along the straight line boundary to form this surface:

Construct the hyperbolic hyperboloid by sweeping the line segment with endpoints [u, u, 1] and [u, -u, -1] as u ranges over the interval [-1, 1].

Construct one-half of a solid cube with one boundary formed by the hyperboloid.

Construct a regular tetrahedron together with the edges of a cube whose vertices includes all the vertices of the tetrahedron.

Construct a regular hexagon cross-section of the cube.