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|Bowers style acronym||Dyad|
|Coxeter diagram||x ()|
|Measures (edge length 1)|
|Number of external pieces||2|
|Level of complexity||1|
|Abstract & topological properties|
|Symmetry||A1, order 2|
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.
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.
Coordinates for the vertices of a line segment of length 1 are simply the points:
The dyad has two distinct representations:
- x (full symmetry, vertices are the same)
- oo&#x (vertices considered of different types)
- ↑ Bowers, Jonathan. "Regular Polytela and Other One Dimensional Shapes".
- ↑ Johnson, Norman W. Geometries and transformations. p. 224.
- Bowers, Jonathan. "Regular Polytela and Other One Dimensional Shapes".
- Wikipedia Contributors. "Line segment".
- Hi.gher.Space Wiki Contributors. "Digon".