Why are $10$-sided dice not bipyramids?

Question

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.

Answer 1

A pentagonal bipyramid would work fine. The problem is that reading the result would be difficult.

Dice roll on a surface and land on one of the faces, then you read the result (usually) on the face on top of the die (the standard d4 would be an exception).

If you make a pentagonal bipyramid and it lands on one of the faces, however, the top of the die is an edge!

This holds for any shape that has an odd number of sides along is mid-section: if you make a bipyramid, it's going to end up with an edge up when you roll it.

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This is what such a die would look like In the left picture, the result is a 4, in the right it's a 5. Not very convenient; but it works!

Answer 2

IF the dice was a biyramid, THEN it would happen the same as the D4: the number cannot be on the faces (if you want to see the result above the dice), in the D4 it would be on every point, and in your new D10, in every edge that shares 1 of its ends to 4 other edges (5 edges in total) But it works! Awfully, but it works!

BUT the old D10 is able to have the numbers on the faces with no problem! That why he joined the Platonic Solids to be all together the dices we know and love...