Uniform Prism is Uniform Polyhedron

Theorem

Let $P$ be a uniform prism.

Then $P$ is a uniform polyhedron.


Proof

Recall the definition of Uniform Polyhedron:

A uniform polyhedron is a polyhedron:

$(1): \quad$ which is isogonal
$(2): \quad$ whose faces are all regular polygons (but not necessarily all of the same type).


Recall the definition of Uniform Prism:

A uniform prism is a regular prism whose lateral faces are square.


From Uniform Prism is Isogonal, $P$ is isogonal.

That all the faces of $P$ are regular polygons follows a fortiori from the definition of regular prism.

Hence the result.

$\blacksquare$


Sources

  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): polyhedron: 1. (plural polyhedra)
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): polyhedron: 1. (plural polyhedra)
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