In geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, an apeirogonal antiprism or infinite antiprism is the arithmetic limit of the family of antiprism

Antiprism

In geometry, 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...

s; it can be considered an infinite polyhedron

Polyhedron

In elementary geometry a polyhedron is a geometric solid in three dimensions with flat faces and straight edges...

 or a tiling

Tiling

Tiling may refer to:* The physical act of laying tiles* The mathematics of tessellations* The compiler optimization of loop tiling* In computing, a tiling window manager, where windows do not overlap...

 of the plane.

If the sides are equilateral triangles, it is a uniform tiling

Uniform tiling

In geometry, a uniform tiling is a tessellation of the plane by regular polygon faces with the restriction of being vertex-uniform.Uniform tilings can exist in both the Euclidean plane and hyperbolic plane...

. In general, it can have two sets of alternating congruent isosceles triangle

Triangle

A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....

s, surrounded by two half-planes.

Related tilings

It can be constructed by an alternation operation applied to an apeirogonal prism

Apeirogonal prism

In geometry, an apeirogonal prism or infinite prism is the arithmetic limit of the family of prisms; it can be considered an infinite polyhedron or a tiling of the plane....

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