Spindown Polyhedra

Magic: the gathering is a trading card game published by Wizards of the Coast [1]. The aim of most variants of the game is to reduce your opponent's life total from twenty to zero, thus winning the game. As it may take several turns to reduce a player's life total to zero, players need a mechanism to keep track of their current life total. For this purpose, players often use a device called a spindown life counter, shown in Figure 1. A spindown life counter is an icosahedron with a special labelling of the faces, such that − starting with 20 life total − a player can reduce their life total in decrements of one by rolling the icosahedron onto an adjacent face each time. A spindown life counter appears similar to a standard icosahedral die, known in gaming as a d20; however, the labelling of faces is different, as also shown in Figure 1.