Waclaw Sierpinski (1882-1969) was one of the most influential mathematicians of his time in Poland and had a worldwide reputation. In fact, one of the moon's craters is named after him. The basic geometric construction of the Sierpinski gasket (and this pyramid) goes as follows. We begin with a triangle in the plane and then apply a repetitive scheme of operations to it (a blackened, 'filled-in,' 2-dimensional triangle). Pick the midpoints of its three sides. Together with the old verticies of the original triangle, these midpoints define four congruent triangles of which we drop the center one. This completes the basic construction step. In other words, after the first step we have three congruent triangles whose sides have exactly half the size of the original triangle and which touch at three points which are common verticies of two contiguous trianges. Now we follow the same procedure with the three remaining triangles and repeat the basic step as often as desired. That is, we start with one triangle and then produce 3, 9, 27, 81, 243, ... triangles, each of which is an exact scaled down version of the triangles in the preceeding step. The above information is courtesy of Ian and Linda Kaplan @ Bearcave.com. Thanks to the Kaplans' and Bear Products! ...and thanks to you for looking, have an awesome day!