The Mathematics of Rubik's Cubes -
Higher-dimensional versions of the familiar Rubik's cube have received renewed attention in recent years, especially as 3-dimensional realizations of 4 and 5-dimensional analogues have become available (!).  Some of the underlying mathematical ideas, analyses and visualizations will be described, and I will bring a physical realization of the 2^4 four-dimensional cube (which has about a billion times the number of positions as the familiar 3^3 cube).