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| Pentagonal trapezohedron | |
|---|---|
 Click on picture for large version. | |
| Type | trapezohedra |
| Faces | 10 kites |
| Edges | 20 |
| Vertices | 12 |
| Face configuration | 5,3,3,3 |
| Symmetry group | D5d |
| Dual polyhedron | pentagonal antiprism |
| Properties | convex, face-transitive |
The pentagonal trapezohedron or deltohedron is the third in an infinite series of face-transitive polyhedra which are dual polyhedra to the antiprisms. It has ten faces (i.e., it is a decahedron) which are congruent kites.
It can be decomposed into two pentagonal pyramids and a pentagonal antiprism in the middle.
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During the seventies the first role-playing games and miniature wargames that used percentile-based skills (RuneQuest was the first of them) first used a couple of twenty-sided dice to get random decimal numbers, such as percentages. To do that the players used to roll two twenty-sided dice and then divided the results as if the dice were ten-sided. The typically pentagonal-trapezohedrical ten-sided dice were invented in the late seventies on this purpose and their invention was announced during the 1980 Gen Con.[1]
To improve rolling, the edges are usually rounded or sub-faces introduced by truncation. Each face has two long edges and two short edges. The five odd-numbered faces meet at the common vertex of their long edges. The five even-numbered faces meet at the common vertex of their long edges.
There seems to be a standard configuration for the numbers on 10-sided dice. If one holds such a die between one's fingers at two of the vertices such that the even numbers are on top, and reads the numbers from left to right in a zigzag pattern, the sequence obtained is 0, 7, 4, 1, 6, 9, 2, 5, 8, 3, and back to 0. (In this position, odd numbers appear upside-down.) Opposite sides on such a die total nine.
These dice are often sold in pairs for use as a percentile die. One die will signify tens from 00 through 90, and the other units from 0 to 9. The use of such markings is to generate random numbers from 00 to 99, also known as percentile.
Regular icosahedra with two sides each marked 0 to 9 are also referred to as ten-sided dice, and sometimes preferred due to their more regular shape (see platonic solid) that improves rolling.
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Los sólidos platónicos son conocidos desde la antigüedad y se sabe que al menos las sectas pitagóricas de los siglos V y IV antes de Cristo les atribuían propiedades metafísicas, numerológicas o simplemente religiosas. En lo que se refiere al icosaedro regular había sido utilizado durante la Antigua Roma para la fabricación de dados, como lo demuestran dos dados de veinte caras de la Antigua Roma conservados en el Museo Británico.[1] No se sabe sin embargo para qué actividad fueron fabricados estos dados, si para un juego o para toda otra actividad.
El dado de veinte caras (cuya notación escrita abreviada es «D20») se hizo popular en los años 60 y 70 al ser usado con cada vez más frecuencia por los llamados juegos de guerra, que en esos años empezaban a conocer un gran éxito. Pocos años más tarde, en 1974, el primer juego de rol en ser comercializado, Dungeons & Dragons, basó su sistema de juego en el uso de un dado de veinte caras. Desde entonces el dado de veinte ha tenido y sigue teniendo un papel importante en numerosos juegos de rol. Los dados de veinte pueden ser numerados de «0» a «9» dos veces (con el fin de ser usados como dado de cien) pero en 1980 se inventaron los dados de diez caras[2] para ser usados de este modo así que hoy en día la mayoría de las versiones de dado de veinte se numeran de «1» a «20».
Muchos virus, por ejemplo el virus del herpes, tienen la forma de un icosaedro. Las estructuras virales se construyen en base a unidades proteicas idénticas repetivas varias veces y el icosaedro es la forma más sencilla para ensamblar usando estas subunidades. Se usa un poliedro regular porque puede ser construido por una unidad proteica única usándola una y otra vez; esto ahorra espacio para el genoma vírico. También algunos protistas, en especial algunos radiolarios, tienen forma icosaédrica, como Circogonia icosahedra.
El dado interno de una bola del 8 mágica que tiene 20 respuestas impresas para preguntas de tipo sí-no es un icosaedro regular.
Si cada arista de un icosaedro se reemplaza por una resistencia de un ohmio, la resistencia entre vértices opuestos es de 0.5 ohmios, y entre vértices adyacentes es de 11/30 ohmios.
La proyección de Fuller (o mapa Dymaxion, creado por Richard Buckminster Fuller) es una proyección gnomónica basada en el icosaedro.
El icosaedro es la forma que tiene el «dogic», un juguete parecido al cubo de Rubik.
Un icosaedro aparece como enemigo en el videojuego Kirby 64, se le conoce como Miracle Matter. También en el videojuego Pokemon Platinum hay un objeto con forma de icosaedro llamado Griseous Orb.
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We're now accustomed to straightforward expressions such as 1d8, 2d10, 3d6+2, and so on. Up until 2nd Edition, however, that notation wasn't used. Instead, dice were indicated by their range of results. For example, what's now written as 2d6 was once expressed as 2-12; 3d10 was 3-30.
It's important to remember that when D&D first appeared, hardly anyone was familiar with the "funny dice" used in the game. Few people had even heard of 4, 8, 12, or 20-sided dice, let alone seen them. That made results such as 1-8 doubly puzzling.
Despite its whimsy, this system worked well 95% (1-95) of the time. Things sometimes got interesting, however, when the nomenclature was applied across the board. Sometimes it was just a question of dividing things in your head, as in these examples (remember that in earlier editions, the number of a given monster appearing per encounter was a listed line in their stat block):
And sometimes it was a case of multiple choice answers. The classic example of this was 3-12. Does that mean 3d4 or 1d10+2? In terms of probable results, those are quite different. The same goes for the huge ranges that occurred frequently in the "no. appearing" entries of the Monster Manual:
The second and more important reason was that the ranges weren't always meant as dice rolls. Where weapon damage and hit points were concerned, dice rolls were appropriate. When talking about the number of orcs in an encounter, however, "30-300" didn't necessarily imply a dice roll of any kind. It was more appropriate for the DM to consider the situation and choose a number. The range simply gave the upper and lower bounds that should be considered. And even those could be ignored at the DM's option.
