You can make a fractal by starting with a cube and recursively removing chunks of it. The result is called a Menger sponge. Here’s a picture after four levels of recursion.
What would it look like if you sliced this open? If you cut parallel to one of the faces it looks just like the original object. But if you cut at an odd angle, you’d be surprised. Here’s a New York Times article about the result.
Karl Menger came up with his sponge in 1926, but only recently did someone think to slice one open as in the article.