Apeirogonal prism
Encyclopedia
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.
Thorold Gosset
called it a 2-dimensional semi-check, like a single row of a checkerboard
.
If the sides are square
s, it is a uniform tiling
. In general, it can have two sets of alternating congruent rectangle
s.
composed of three triangles and one apeirogon
at each vertex.
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 prism or infinite prism is the arithmetic limit of the family of prisms
Prism (geometry)
In geometry, a prism is a polyhedron with an n-sided polygonal base, a translated copy , and n other faces joining corresponding sides of the two bases. All cross-sections parallel to the base faces are the same. Prisms are named for their base, so a prism with a pentagonal base is called a...
; 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.
Thorold Gosset
Thorold Gosset
Thorold Gosset was an English lawyer and an amateur mathematician. In mathematics, he is noted for discovering and classifying the semiregular polytopes in dimensions four and higher.According to H. S. M...
called it a 2-dimensional semi-check, like a single row of a checkerboard
Checkerboard
A checkerboard or chequerboard is a board of chequered pattern on which English draughts is played. It is an 8×8 board and the 64 squares are of alternating dark and light color, often red and black....
.
If the sides are square
Square (geometry)
In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles...
s, 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 rectangle
Rectangle
In Euclidean plane geometry, a rectangle is any quadrilateral with four right angles. The term "oblong" is occasionally used to refer to a non-square rectangle...
s.
Related tilings
An alternation operation can create an apeirogonal antiprismApeirogonal antiprism
In geometry, an apeirogonal antiprism or infinite antiprism is the arithmetic limit of the family of antiprisms; it can be considered an infinite polyhedron or a tiling of the plane.If the sides are equilateral triangles, it is a uniform tiling...
composed of three triangles and one apeirogon
Apeirogon
An apeirogon is a degenerate polygon with a countably infinite number of sides. It is the limit of a sequence of polygons with more and more sides.Like any polygon, it is a sequence of line segments and angles...
at each vertex.
