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# Pentagonal antiprism

In geometry, the pentagonal antiprism is the third in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps. It consists of two pentagons joined to each other by a ring of 10 triangles for a total of 12 faces. Hence, it is a non-regular dodecahedron.

Geometry

If the faces of the pentagonal antiprism are all regular, it is a semiregular polyhedron. It can also be considered as a "parabidiminished icosahedron". The two pentagonal faces can be stellated to form the icosahedron.

Relation to polytopes

The pentagonal antiprism occurs as a constituent element in some higher-dimensional polytopes. Two rings of 10 pentagonal antiprisms each bound the hypersurface of the 4-dimensional grand antiprism. If these antiprisms are stellated into pentagonal prism pyramids and linked with rings of 5 tetrahedra each, the 600-cell is obtained.

* Set of antiprisms
* Octahedron Triangle-capped antiprism
* Square antiprism
* Hexagonal antiprism
* Octagonal antiprism

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* [http://polyhedra.org/poly/show/28/pentagonal_antiprism Pentagonal Antiprism: Interactive Polyhedron Model]
* [http://www.georgehart.com/virtual-polyhedra/vp.html Virtual Reality Polyhedra] www.georgehart.com: The Encyclopedia of Polyhedra
** VRML [http://www.georgehart.com/virtual-polyhedra/vrml/pentagonal_antiprism.wrl model]
** [http://www.georgehart.com/virtual-polyhedra/conway_notation.html Conway Notation for Polyhedra] Try: "A5"
* [http://www.lifeisastoryproblem.org/explore/net_pentagonal_antiprism.pdf Printable Net of a Pentagonal Antiprism] [http://www.lifeisastoryproblem.org Life is a Story Problem.org]

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