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 a fortiori regular polygons.

It remains to be shown that $P$ is isogonal.

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Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $13$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $13$
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Archimedean solid
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): prism