Regular Prism is Uniform Polyhedron/Mistake

Source Work

1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.)

2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.):

polyhedron

Right prisms and antiprisms that have regular polygons as bases are also uniform.

Recall the definition of Right Prism:

A right prism is a prism whose lateral edges are perpendicular to the bases.

That is, whose lateral faces are rectangles.

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).

So, while the bases are regular polygons by hypothesis, the lateral faces are not necessarily regular.

Hence it is important to state that such a prism must be a uniform prism:

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

Similarly, an antiprism has lateral faces which, while triangular, are not necessarily equilateral.

In order to rescue this result, it is important to state that such an antiprism must in fact be a uniform antiprism:

A uniform antiprism is an antiprism:

$(1): \quad$ whose bases are both congruent regular polygons

$(2): \quad$ whose lateral faces are all equilateral triangles.

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)