The Sierpinski Sponge is a fractal that lives in 3D space. It is like a triangular pyramid, but it is made out of smaller pyramids, which themselves are made out of smaller pyramids, which themselves are made out of even smaller pyramids, and so on forever.
In 2011 and 2014, we built models of the Sierpinski Sponge out of paper and sticky-tape. Four small pyramids were joined at the corners to make a Stage 1 model. Then four Stage 1 models were joined to make a Stage 2 model. Then four Stage 2 models were joined to make a Stage 3 model, and so on.
The following playlist shows the construction of the Stage 6 model in 2011.