Generating Cube-Like Structures from 3-Tuples of Equidistant Points on a Circle

This Demonstration shows an interesting pattern involving equally spaced points on a circle (top-left graphic). Lists of length three containing two-dimensional points are made by taking the 3-tuples of the points. These points are best shown in 2D by plotting all of the triangles that the lists represent (top-right graphic); they are drawn as overlapping.

When the list of 3-tuples of pairs is transposed, lists of length two containing lists of length three are made. The bottom-left graphic shows what that list looks like projected into 2D, and the bottom-right graphic shows what that list looks like in 3D. Interesting square or cube-like structures are generated, depending on the original number of points.

This Demonstration shows that by doing simple matrix operations onto equally spaced points on a circle, fascinating cube-like structures can be generated. Other interesting results can be obtained if the lists are transposed into four dimensions by using 4-tuples. Another interesting extension would be to use equally spaced points on a sphere.