Ray

Ray
Rank	1
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Ray
Elements
Vertices	1
Vertex figure	Point
Measures
Length	$\infty$
Central density	1
Related polytopes
Dual	Ray
Abstract & topological properties
Flag count	1
Euler characteristic	1
Surface	Point
Orientable	Yes
Properties
Symmetry	I, order 1
Convex	Yes
Nature	Tame

The ray is a geometric object consisting of a point and a line extending indefinitely in one direction. Although it shares many properties with polytopes it is generally not considered a polytope.

Abstract

The elements of a ray form a ranked and bounded poset, however they do not meet the diamond property and thus the ray is not an abstract polytope. Polytopoids that fail the diamond property are often called exotic, so the ray can be thought of as an exotic 1-polytope. It is the smallest possible rank 1 poset.

While it itself is not a polytope, a compound of two rays is abstractly a dyad, making it the only ranked and bounded poset that has a non-trivial compound which is an abstract polytope. The dyad does not meet the definition for a compound and thus, rather paradoxically, compounds of rays are not considered compounds. Geometrically a compound of two rays is an antidyad.

See also

• Monogon

External links

• Wikipedia Contributors. "Ray (geometry)".
• Bowers, Jonathan. "Regular Polytela and Other One Dimensional Shapes".