Is a polyhedron with different prime length edges possible? Can a polyhedron be constructed  with all its  edges of different prime number length ? A primahedron maybe ? Is there a limit or constraint on the number of such polyhedra, similar to the limit of 5 Platonic regular solids?
 A: *

*For the elementary case of a tetrahedron, the smallest one you can consider is:

$$3,5,7,11,13,17$$
In this reference, you will find its folding pattern:

In fact, many others can be constructed (maybe an infinity of them), for example:
$$13, 17, 19,23,29,31$$
Indeed, considering triangle with sides $13,17,19$ as the base triangle, strict triangle inequalities are valid for the 3 other facets:
$$(13,23,27), \ \ (17,27,31), \ \ (19,31,23)$$


*The farthest you take, in the table of primes, $6$ consecutive primes, the more "almost-equilateral" the facets will be , with a guarantee that all triangle inequalities are checked...


*The case of a hexahedron (volume with six faces): build two tetrahedra in the manner seen above with the same base, then glue them on this common base.


*This "gluing" method could be extended to more general polyhedra (with the possibility that the generated polyhedron isn't convex).


*About "stacked polyhedra", in particular stacked (or glued) tetrahedra, see here.
