antiprism

An antiprism is a prismatoid whose bases are congruent and whose lateral faces are congruent triangles.

An antiprism can be used to construct an icosahedron: Let $A$ be an antiprism with regular pentagons as its bases and equilateral triangles as its lateral faces. To each base of $A$, attach a pentagonal pyramid whose base is congruent to the bases of $A$ and whose lateral faces are equilateral triangles.

For any integer $n\ge 3$, the following are equivalent statements about an antiprism $A$:

1. $A$ has a base that is an $n$-gon;

2. $A$ has $2n+2$ faces;

3. $A$ has $2n$ vertices;

4. $A$ has $4n$ edges.