Extensive dice collection (d4, d6, d8, d10, d12, d14, d20, d24, d28, d30, d48, d60, d120)
Description
This is an extensive collection of dice. It contains all Catalan solids and some other forms. The labelling of the dice are numerically balanced (as far as possible). There are some alternative labellings available depending on which aspect you think is more important. <b> Balanced labellings </b> Here are the aspects which I considered for labelling: - balancing opposed faces: this means that the number on one face of the dice and the one on the opposite face add up to the same value (7 for a d6, 9 for a d8, 31 for a d30, ... N+1 for a N-sided dice,...) - balancing vertices: this means that the faces which share a common vertex will add up to the same value. This is not always possible to achieve [as soon as there are an odd number of faces touching a vertex], but one can then try to minimise it. - balancing halves: there are more (or less) natural ways to group the faces of the dice to cut the dice in two halves. The sum should be as close to N×(N+1)/4 as possible (for an N-sided dice) <b>3 Categories</b> The name of solid (most often a Platonic or Catalan solid) is given in the filename. There are 3 series of files: - filename begins with the letter "d": these are mostly the common dice. There are some unusual alternative forms for the d12 and d24 as well as the unusual d14 and d28. - filename begins with the letter "e": these are the usual dice with 48 and 120 sides as well as one of the d60. I did not look for specific labellings for these dice. - filename begins with the letter "f": these solids have the following particularity. When the die is at rest, then one face is horizontal (the one on the table), but there is no opposite face which is also horizontal. The number is nevertheless engraved on the top, so that one can read it (see the d60 in the previews). For such solids, balancing opposed faces makes no sense. This series include some unusual d6, d8, d10, d12, d16, d24 and d60. <b>"Roll-ability"</b> Two options are available to make the dice roll better. One of them is chamfering the edges, the other is to intersect with a ball. The latter is good for dice with 12 sides or less (with the exception of the standard d12 [dodecahedron]) as well as one of the d24 [triakis octahedron]. See the d12 in the previews for an example of intersection with a ball. You can combine both effects if desired. <b>Fonts</b> It is possible to use a different font to write the numbers on the dice (and also write other things as numbers). I included an extra font in the files (see the d30 in the previews). The font is designed so that the numbers all cover the same area. This means that in theory, no unbalance is created by writing some number, rather than another on a specific face (you need to write 06 instead of 6 if there are some 2-digit numbers on the dice). <b>Fairness</b> I seriously doubt that the font have a significant impact on the balance on the die. Imperfection in the printing have a larger impact. There is a rule of thumb, that you should throw a N-sided dice roughly (N-1)×1000 times to get an idea whether it is fair or not. Contrary to all dice in the "d" series, the d28 is not face-transitive. This means that there is no theoretical proof of its fairness. <b>Source</b> The source of the coordinates for the solids is (with some rare exceptions) <a href="http://dmccooey.com/polyhedra/"> dmccoey's visual polyhedra website</a>.
Statistics
Likes
169
Downloads
0