The 3D kaleidoscope

The author presents a method for constructing platonic solids that takes advantage of their symmetry. This works well with a coordinate transform system, since symmetry is based on coordinate transformations. He treats the cube and other related shapes, using a seed-triangle element that can be rotated and reflected to generate the shape. He shows that the seed triangle can be replaced with any shape whatever, and all the replications will generate a result that also shares the symmetry of the cube. By making the seed shape rotate and move about in some random way, a changing shape that generates the 3-D kaleidoscope patterns of the title can be animated. The tetrahedron is also treated.<>