A famous fractal solid that is the three-dimensional
equivalent of the Sierpinski carpet
(which, in turn, is the one-dimensional equivalent of Cantor
dust). To make a Menger sponge, take a cube, divide it into 27 (= 3
× 3 × 3) smaller cubes of the same size and remove the cube in
the center and the six cubes that share faces with it. What's left are the
eight small corner cubes and twelve small edge cubes holding them together.
Now, imagine repeating this process on each of the remaining 20 cubes. Repeat
it again. And again ... ad infinitum. The Menger sponge was invented in
1926 by the Austrian mathematician Karl Menger (1902–1985).
AND PATHOLOGICAL CURVES