If we let sides be different lengths, we can have a prism which is like anew (unsharpened) pencil with flat sides. Often pencils have just 6 flat sides, and we roll the pencil so that any sideis likely to be face up. We can imagine a pencil with 8 sides, or 7 or even 27.If we have an odd number of sides, no one face is "up" (consider a triangular cross-sectionedpencil for instance, with just 3 choices of side). Here we may agree to use the side thatthe pencil lands on. Kids will flex their fine motor skill muscles in cutting, folding and pasting this resource. Getting in loads of practice for writing later on. What can I use this 12 sided dice for?

Unlike other common dice, a four-sided (tetrahedral) die does not have a side that faces upward when it is at rest on a surface, so it must be read in a different way. On some four-sided dice, each face features multiple numbers, with the same number printed near each vertex on all sides. In this case, the number around the vertex pointing up is used. Alternatively, the numbers on a tetrahedral die can be placed at the middles of the edges, in which case the numbers around the base are used. There are other shapes if we don't insist that all the sides are the same length ORwe allow 2-D shapes, but which still are fair dice - i.e. each number on a faceis as likely as any other number to turn up. If we used pentagons then the bi-pyramidal dice would be 10-sided.It would be useful for generating random numbers up to 10. Kybos, Alea. "Properties of Dice" (PDF). Archived from the original (PDF) on 28 May 2012 . Retrieved 7 October 2012. Weisstein, Eric W. "Dice". MathWorld. – analysis of dice probabilities, also featuring Uspenski's work on rolling multiple dice

A puzzle I came across when I was 12 is a box of the 12 pentominoes, each piece being one of the ways of "tearing 5 connected square stamps from a perforated sheet" as George Martin puts it. They fit into a variety of shaped boxes but mine came in a 10x6 box. They can be fitted into it in 2339 different ways (ignoring rotations and horizontal and vertical flips of the box).

Horridge, Kevin (27 November 2017). "6 Ways Casinos Stop Dice Cheats". Casino.org . Retrieved 11 October 2019. Raoul Martens recommends an article in German on Kepler'sinterest in the Platonic solids: Die kosmische Funktion des Goldenen Schnitts by Theodor Landscheidt in Sterne, Mond, Kometen, Bremenund die Astronomie zum 75. Jahrestag der Olbers-Gesell-schaft Bremen e.V. Verlag H. M. Hauschild, Bremen 1995. Dice are often sold in sets, matching in color, of six different shapes. Five of the dice are shaped like the Platonic solids, whose faces are regular polygons. Aside from the cube, the other four Platonic solids have 4, 8, 12, and 20 faces, allowing for those number ranges to be generated. The only other common non-cubical die is the 10-sided die, a pentagonal trapezohedron die, whose faces are ten kites, each with two different edge lengths, three different angles, and two different kinds of vertices. Such sets frequently include a second 10-sided die either of contrasting color or numbered by tens, allowing the pair of 10-sided dice to be combined to generate numbers between 1 and 100. An Icosahedron in an Octahedron Using the same three golden rectangles at right-angles to each other, we can also make an octahedron.The probability of rolling at least X same values (equal to y) out of the set — the problem is very similar to the prior one, but this time the outcome is the sum of the probabilities for X=2, 3, 4, 5, 6, 7. Moving to the numbers, we have: P = P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) = 0.11006 = 11.006%. As you may expect, the result is a little higher. Sometimes the precise wording of the problem will increase your chances of success. For example, if you need a d12 die with 12 sides for your last role-playing battle with your friends, you are in the right place to get a clean roll that will allow you hours of fun without having to worry about the dice. all the faces are identical in shape and size Coordinates and other statistics of the 5 Platonic Solids They are the tetrahedron, cube (or hexahedron), octahedron, dodecahedron and icosahedron. A sphere containing another sphere with 100 facets flattened into it. Note that this design is not isohedral; it does not function as a uniform fair die as some results are more likely than others. Using Unicode characters, the faces can be shown in text using the range U+2680 to U+2685 or using decimal ⚀ to ⚅. [26] Loaded dice [ edit ]

It includes all our 5 Platonic solids, and,since it also includes those where not every edge is the same length, it includes the bi-pyramids too. Every face is identical toevery other face, so all the faces have exactly the same polygonal shape, but some edges have different lengths to others. There are others apart fromthe Platonic solids and the bi-pyramids and are some pretty weird too!A popular gambling game from at least Roman times involved throwing dice and is also called casting the dice. Some of the Roman soldiers "cast lots" for the clothes of Jesus at his crucifiction. Today we still use the phrase the die is cast. I used to think this phrase meant that a mould (US spelling=mold) had been made since we also read of someone being cast in the heroic mould as if they had been molten metal poured into a mould from which they solidify into a heroic shape. However I was wrong and it is just another use of the word die. The probability of rolling all the values equal to or higher than y – the problem is similar to the previous one, but this time p is 1/s multiplied by all the possibilities which satisfy the initial condition. For example, let's say we have a regular die and y = 3. We want to rolled value to be either 6, 5, 4, or 3. The variable p is then 4 · 1/6 = 2/3, and the final probability is P = (2/3) n.