Extensive dice collection (d4, d6, d8, d10, d12, d14, d20, d24, d28, d30, d48, d60, d120)

thingiverse

This is an extensive collection of dice, featuring all Catalan solids and various forms. The labeling on each die is carefully balanced to ensure numerical consistency, with alternative options available depending on your preferences. Balanced Labeling Options ------------------------ Here are the considerations taken into account for labeling: * Balancing Opposed Faces: Each face is paired with its opposite, ensuring their numbers add up to a consistent value (7 for a d6, 9 for a d8, etc.). * Balancing Vertices: The faces sharing a common vertex are balanced, with each group adding up to the same value. When this is not possible due to an odd number of faces, the imbalance is minimized. * Balancing Halves: Faces are grouped into halves, and their sums aim to be as close as possible to N×(N+1)/4 for an N-sided die. 3 Categories ------------ The filename indicates the type of solid, often a Platonic or Catalan solid. There are three series of files: * Filename starts with "d": These include common dice, such as the d12 and d24, along with some unusual forms like the d14 and d28. * Filename starts with "e": This series features dice with 48 and 120 sides, including one d60. Specific labeling was not explored for these dice. * Filename starts with "f": These solids have a unique characteristic: when at rest, one face is horizontal, but there is no opposite face that is also horizontal. The top face is engraved with the number, allowing it to be read (see the d60 preview). For such solids, balancing opposed faces makes no sense. This series includes unusual d6, d8, d10, d12, d16, d24, and d60. Roll-ability Options ------------------- Two options can enhance the dice's rollability: * Chamfering edges: A technique to make the dice roll more smoothly. * Intersect with a ball: Good for dice with 12 sides or less (excluding the standard d12) as well as one of the d24. See the d12 preview for an example. Fonts ------ A different font can be used to write numbers on the dice, and additional text can be written as numbers. An extra font is included in the files (see the d30 preview). This font ensures that all numbers cover the same area, minimizing unbalance caused by writing certain numbers over others (e.g., 06 instead of 6 for two-digit numbers). Fairness --------- The font's impact on balance is minimal compared to printing imperfections. A rule of thumb suggests throwing a N-sided dice approximately (N-1)×1000 times to determine its fairness. The d28, unlike all dice in the "d" series, is not face-transitive, meaning there is no theoretical proof of its fairness. Source ------- The coordinates for the solids come from dmccoey's visual polyhedra website, with some rare exceptions.