Dyad

The dyad, ditelon, dion or simply line segment, is the only possible 1-polytope (rarely polytelon). Its facets are two points. It appears as the edges of all higher polytopes.

Dyad
(OFF file)
Rank	1
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Dyad
Coxeter diagram	x ()
Schläfli symbol	{}
Tapertopic notation	1
Toratopic notation	I
Bracket notation	I
Elements
Vertices	2
Vertex figure	Point
Measures (edge length 1)
Circumradius	$\frac12 = 0.5$
Length	1
Central density	1
Number of external pieces	2
Level of complexity	1
Related polytopes
Army	Dyad
Dual	Dyad
Conjugate	None
Abstract & topological properties
Flag count	2
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	A1, order 2
Convex	Yes
Nature	Tame

A dyad is simultaneously the 1-simplex, the 1-hypercube, and the 1-orthoplex. Furthermore, a dyad is the pyramid, prism, tegum, ditope, and hosotope of the point. It may also be considered a 0-hypersphere.

Congruent dyads can tile 1D space as the regular apeirogon.

Vertex coordinates

Coordinates for the vertices of a line segment of length 1 are simply the points:

• $\left(\pm\frac12\right).$

Representations

The dyad has two distinct representations:

• x (full symmetry, vertices are the same)
• oo&#x (vertices considered of different types)

External links

• Bowers, Jonathan. "Regular Polytela and Other One Dimensional Shapes".

• Wikipedia Contributors. "Line segment".
• Hi.gher.Space Wiki Contributors. "Digon".

• Hartley, Michael. "{}*2".