Pentagonal trapezohedron

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Pentagonal trapezohedron
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Type	trapezohedra
Faces	10 kites
Edges	20
Vertices	12
Face configuration	5,3,3,3
Symmetry group	D_5d
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 polyhedron to the antiprisms. It has ten faces (i.e., it is a decahedron) which are congruent kites. The basic shape is two five-sided pyramids stuck together on their pentagonal face, one rotated by 36 degrees.

[edit] As a die

Ten-sided die

Some role-playing games and miniature wargames use ten-sided dice, typically pentagonal trapezohedra, to get random decimal numbers, such as percentages. To improve rolling, the edges are usually rounded or sub-faces introduced by truncation.

Each face has two long sides and two short sides. The five odd-numbered faces meet at the common vertex of their long sides. The five even-numbered faces meet at the common vertex of their long sides.

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 be marked by tens from 00 through 90, and the other will have units from 0 to 9. The use of such markings is to generate random numbers from 00 to 99, also known as percentile. In practice, two dice of different colors are usually easier to read; however, having a specifically marked tens die prevents players from being able to vacillate over which die they "meant" to represent the tens digit after receiving the results of the roll.

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.