This LEGO creation grew out of simple play with some parts to see how they could connect together to form shapes. Starting with simple blocks small shapes emerged that grew into larger shapes. Soon it because clear that one simple piece (called "headlight") could be used to form large complicated recursive structures. Small Menger sponges were constructed and connected to make larger Menger sponges which were then further refined, leading to the current level-3 Menger sponge. The result is a structure which comes across much larger than the physical dimensions would indicate and gives an opportunity to experience what a Menger sponge is like including the fractal nature.
A level-3 Menger sponge created using approximately 32,000 LEGO bricks (all of the type known as "headlight"). This was built at the Iowa State University 2022 REU in Mathematics with the main build team consisting of Steve Butler, Elena D'Avanzo, Laura P. Gamboa Guzmán, Rachel Heikkinen, Joel Jeffries, Alyssa Kruczek, and Harper Niergarth