An antiprismMathworldPlanetmath is a prismatoidMathworldPlanetmath whose bases are congruent and whose lateral faces are congruent trianglesMathworldPlanetmath.

An antiprism can be used to construct an icosahedronMathworldPlanetmathPlanetmath: Let A be an antiprism with regular pentagons as its bases and equilateral trianglesMathworldPlanetmath 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 n3, the following are equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmath 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
Canonical name Antiprism
Date of creation 2013-03-22 16:57:02
Last modified on 2013-03-22 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