For more info about Menger sponges, see this other design.

This is a model of a level 1 Menger sponge with base cubes ( which are not menger sponges in themselves ) with a size of 3 brick units. The hooks sticking out of the edges are meant to combine twenty of these into a level 2 Menger sponge. However, because of the hooks, the level 2 Menger sponge, mathematically is not exactly a Menger sponge. This is because the hooks exist between the level 1 and level 2 sponges, but not between level 1 and the base cubes.

This 3L version can also be made in dark and light bluish gray, blue, red and perhaps in white and other colors, but not in lime ( there is no 9L liftarm in lime ) and not in yellow ( because there is no 1 x 1 liftarm in yellow ).

To combine these level 1 sponges into a level two, connect them with 7L or 8L axles. They will stay in place by themselves because of the axle holes in some of the hooks.

13 October 2023