Square-Sided Prism is Semiregular Polyhedron

Theorem
A square-sided prism is a semiregular polyhedron.

Proof
Let $P$ be a square-sided prism.

By definition, $P$ is regular.

Hence the bases of $P$ are regular polygons.

Also by definition, the lateral faces of $P$ are square so regular polygons.

It remains to be shown that $P$ is vertex-transitive.