Menger sponge

The Menger sponge is a mathematical object formed by starting with a cube, and then through each direction drilling a hole down the center. The result can be thought of as 20 cubes put together and now we repeat the process with each of those cubes, and so forth and so on. This makes a simple example of what is known as a fractal (or fractional dimensional object, in this case the dimension is 2.7268...=log(20)/log(3)).

I found a way to build some smaller Menger sponges via LEGO, and in particular using only one part (4070 commonly known as "headlight"). Using ~32,000 pieces and the help of the ISU REU 2022 students we were able to successfully build a level 3 Menger sponge.