## Skew dice

Monday Math Day?! Meet Robert Fathauer and Henry Segerman, authors of the Dice Lab and creators of “skew dice” (pictured below)–strange-looking dice that still generate fair odds. In their words: “When tossed, a fair die yields its various numbers or symbols with equal probability, regardless of details of the surface or the toss. The shapes of dice are based on polyhedra, solids whose faces are polygons. To ensure fairness, each face of the polyhedron should have an identical relationship to the other faces …”

Just in case, here is a short explanation of the mathematics of their skew dice: “Considerable thought went into the numbering of the dice. The starting point was locating the largest number opposite the smallest number (on opposing faces), the next largest opposite the next smallest, etc. This convention is widely followed in dice design. The next priority was to distribute the numbers as uniformly as possible. That was accomplished by balancing the sums of the numbers on each group of faces surrounding a vertex … Note that the average numerical value per face for an n-sided die is (n + 1)/2.” (Hat tip: Cliff Pickover.)