Commonly used $10$-sided dice are pentagonal trapezohedrons, as opposed to pentagonal bipyramids. Given that bipyramids are a more "obvious" shape for a fair die with an even number of faces, it's curious to me that the trapezohedrons are the more commonly used shape.
So, what are the advantages, if any, of trapezohedrons over bipyramids for making fair dice? Specifically, are there any meaningful differences in the symmetry properties of these shapes?
Note: the name "trapezohedron" is misleading, at least in the USA. The faces are actually kites, as if we had removed two opposing faces of a pentagonal (regular) dodecahedron and extended the remaining faces to close the gap.