One of the proposed exhibits for the Museum of Mathematics involves a Menger sponge, a geometric object devised by a mathematician named Karl Menger in 1926.

The Menger sponge consists of a cube with square holes, arrayed in a fractal pattern, through the top and the sides.

“It’s a well-known object that people have studied for a long time,” said George Hart, the museum’s chief of content. “But it’s only recently that anyone thought to slice it in this interesting way.”

In the proposed exhibit, a visitor can pull apart the two pieces of the Menger sponge and discover that the holes along the diagonal are not squares, but six-sided stars. "It's like a 'gosh, that's really cool' kind of emotion people have," Dr. Hart said. "It's a very nice example of how mathematics can give you these big surprises."