| Pentagonal trapezohedron | |
|---|---|
| Type | trapezohedra |
| Faces | 10 kites |
| Edges | 20 |
| Vertices | 12 |
| Face configuration | 5,3,3,3 |
| Symmetry group | D5d, [2+,10], (2*5) |
| 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. It can also be decomposed into two pentagonal pyramids and a Dodecahedron in the middle.
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During the 1970s 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. On the other hand, 20-sided dice labeled with single digits -twice in a row- are still nowadays commercialized, as they were back in the seventies. Although it is claimed the typically pentagonal-trapezohedrical ten-sided dice were invented in the late seventies (their invention was announced during the 1980 Gen Con)[1] the US patent office has a patent[2] showing a similar die dated 1906.
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. "00" is sometimes read as 0 and sometimes as 100, depending on the game system being used, just as "0" a single die is sometimes treated as a roll of 10.
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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