Level 3 requires ~32000 LEGO pieces
Level 2 requires 1968 LEGO pieces
Level 1 requires 120 LEGO pieces
Looking through the center of a level 3 Menger sponge.
The construction is so symmetric that the center of mass is in the exact middle of the cube. This allows the Menger sponge to perfectly balance on a corner. (Also can double as an earthquake detector.)
If we combine the Menger sponge together with the compliment of the Menger sponge (=what we take out to make the Menger sponge), we get the whole cube back.
LEGO banana man to help give a sense of the scale of the level 3 Menger sponge.
The two different approaches to building a level 2 Menger sponge. On the left is one built directly without all of the internal parts (takes 1968 pieces, though if trapped on a desert island you can make do with 1944 pieces). On the right is one built by combining 20 level 1 Menger sponges together (takes 2400 pieces, and is a bit blockier (hurts more if you drop it on your foot).
A level 1 Menger sponge that has exploded.
A level 2 Menger sponge that has exploded.
Menger sponge built out of transparent bricks.
The assembly line crew for building a corner of the level 3 Menger sponge.
Having fun with building a corner. No need to stress, it is just LEGO.
The 2022 ISU REU group that helped build the level 3 Menger sponge. Special thanks to Joel Jeffries, Elena D'Avanzo, Rachel Heikkinen, Alyssa Kruczek, Harper Niergarth, and Laura Gamboa Guzman who went above and beyond in putting the Menger sponge together.