This fractal is called a Sierpinski Tetrahedron. A tetrahedron is a polyhedron that has four faces. (The plural of tetrahedron is tetrahedra.) The small tetrahedra form four medium-sized tetrahedra: blue, red, yellow, and green. The medium-sized tetrahedra form one large tetrahedron.

How many small faces does this fractal have? Be sure to include faces you can’t see as well as those you can. Try to find a way to figure this out so that you don’t have to count every face.
How many small tetrahedra are in the bottom layer, touching the table?
To make an even bigger version of this fractal, you could take four fractals like the one pictured and put them together. Explain where you would attach the fractals to make a bigger tetrahedron.
How many small faces would this bigger fractal have? How many small tetrahedra would be in the bottom layer?
What other patterns can you find?