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.
Title  antiprism 

Canonical name  Antiprism 
Date of creation  20130322 16:57:02 
Last modified on  20130322 16:57:02 
Owner  Wkbj79 (1863) 
Last modified by  Wkbj79 (1863) 
Numerical id  9 
Author  Wkbj79 (1863) 
Entry type  Definition 
Classification  msc 51M20 
Classification  msc 51M04 