Square-Sided Prisms are Countably Infinite

Theorem

There is a countably infinite different varieties of square-sided prisms.

Proof

By definition, a square-sided prism is made of:

$2$ bases which are regular polygons

as many lateral faces as there are sides of one of the bases.

Hence for each type of regular polygon there exists a corresponding square-sided prism.

There exists a type of regular polygon for each natural number greater than or equal to $3$.

There exists countably infinite set of natural numbers greater than or equal to $3$.

Hence the result.

$\blacksquare$