# 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 $n\geq 3$, the following are equivalent statements about an antiprism $A$:

1. 1.

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

2. 2.

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

3. 3.

$A$ has $2n$ vertices;

4. 4.

$A$ has $4n$ edges.

Title antiprism Antiprism 2013-03-22 16:57:02 2013-03-22 16:57:02 Wkbj79 (1863) Wkbj79 (1863) 9 Wkbj79 (1863) Definition msc 51M20 msc 51M04