Analogously, in three dimensions, draw a cube and inside it a sphere that touches all six sides. The circle takes up 79% of the square, but the sphere only takes up 52% of the cube. The pattern ...

The only thing we can predict right now is where the Cube is going. I would be amazed if it deviates from this path, though whether it goes south or southwest after Lazy Links is not yet clear.

In honor of the toy's 40th anniversary, the Liberty Science Center in Jersey City, N.J., is launching an exhibition devoted to the puzzle.

Similarly, in our familiar three-dimensional universe, if a four-dimensional ball were to pass through it would appear as a point, grow into a solid ball, eventually reach its full radius, then ...

In 1974, Hungarian architecture professor Ernő Rubik created a three-dimensional cube to teach his students about three-dimensional spaces. That cube later became one of the most famous toys ...

In the illustration: A tesseract (a four-dimensional cube) and the "shadow" it casts on a plane—the quasicrystal discovered by Shechtman. According to Prof. Bartal, "The fact that a quasicrystal ...