# Pentagonal antiprism

In

geometry , the**pentagonal antiprism**is the third in an infinite set ofantiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps. It consists of twopentagon s joined to each other by a ring of 10triangle s for a total of 12 faces. Hence, it is a non-regulardodecahedron .**Geometry**If the faces of the pentagonal antiprism are all regular, it is a

semiregular polyhedron . It can also be considered as a "parabidiminishedicosahedron ". The two pentagonal faces can bestellated to form the icosahedron.**Relation to polytopes**The pentagonal antiprism occurs as a constituent element in some higher-dimensional

polytope s. Two rings of 10 pentagonal antiprisms each bound the hypersurface of the 4-dimensionalgrand antiprism . If these antiprisms are stellated into pentagonal prism pyramids and linked with rings of 5 tetrahedra each, the600-cell is obtained.**See also*** Set of antiprisms

*Octahedron Triangle-capped antiprism

*Square antiprism

*Hexagonal antiprism

*Octagonal antiprism **External links***

* [*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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**Pentagonal trapezohedron**— The pentagonal trapezohedron or deltohedron is the third in an infinite series of face transitive polyhedra which are dual polyhedron to the antiprisms. It has ten faces (i.e., it is a decahedron) which are congruent kites. It can be decomposed… … Wikipedia**Antiprism**— An n sided antiprism is a polyhedron composed of two parallel copies of some particular n sided polygon, connected by an alternating band of triangles. Antiprisms are a subclass of the prismatoids.Antiprisms are similar to prisms except the bases … Wikipedia**Grand antiprism**— (Schlegel diagram wireframe) Type Uniform polychoron Uniform index 47 Cells 100+200 (3.3.3) … Wikipedia**Octagonal antiprism**— Uniform Octagonal antiprism Type Prismatic uniform polyhedron Elements F = 18, E = 32 V = 16 (χ = 2) Faces by sides 16{3}+2{8} … Wikipedia**Gyroelongated pentagonal pyramid**— Type Johnson J10 J11 J12 Faces … Wikipedia**Square antiprism**— In geometry, the square antiprism is the second in an infinite set of antiprisms formed by an even numbered sequence of triangle sides closed by two polygon caps.If all its faces are regular, it is a semiregular polyhedron.When eight points are… … Wikipedia**Hexagonal antiprism**— In geometry, the hexagonal antiprism is the 4th in an infinite set of antiprisms formed by an even numbered sequence of triangle sides closed by two polygon caps.If faces are all regular, it is a semiregular polyhedron. See also * Set of… … Wikipedia**Heptagonal antiprism**— Infobox Polyhedron with vertfig Polyhedron Type=Semiregular polyhedron Face List=16 triangles 2 heptagons Edge Count=21 Vertex Count=14 Wythoff Symbol= 2 2 7 Symmetry Group=D7d Vertex List=3.3.3.7 Dual=Heptagonal trapezohedron Property… … Wikipedia**Compound of six pentagonal antiprisms**— Type Uniform compound Index UC27 Polyhedra 6 pentagonal antiprisms Faces … Wikipedia**Gyroelongated pentagonal birotunda**— Infobox Polyhedron with net Polyhedron Type=Johnson J47 J48 J49 Face List=4x10 triangles 2+10 pentagons Edge Count=90 Vertex Count=40 Symmetry Group=D5 Vertex List=2x10(3.5.3.5) 2.10(34.5) Dual= Property List=convex, chiral Net In geometry, the… … Wikipedia