This is a Rubik’s cube of my own design. It’s made from 156 squares of paper, and other things I had on my desk. The Rubik’s cube is a popular example of Group Theory in real life.
The set of all ways to assemble a cube from the Rubik’s cube pieces has cardinality (12!)(2^12)(8!)(3^8) because there are 12 edge pieces each with 2 possible orientations, and 8 corner pieces each with 3 possible orientations. However, many of these configurations are impossible to reach by turning a solved cube. So the actual Rubik’s cube group has “only” (12!)(2^10)(8!)(3^7)=43,252,003,274,489,856,000 elements.
Romy Williamson is an undergraduate student at Merton College.