Fractal tetrahedra: What's left in, what's left out, and how to build one in four dimensions

摘要

We investigate several projections of the Sierpinski hypertetrahedron and observe that the iterative construction of the hypertetrahedron gives rise to an iterative construction of the projections. In addition, we show that the complements of these projections give some insight into the structure of the hypertetrahedron. Finally, we show that projections into three dimensions of fractals in four dimensions can give rise to collections of new fractals.