Point

The point (also called monad or monon). is the only possible 0-polytope or polyon. If the nullitope is not considered, this is the simplest possible polytope overall, as it has no other lower-dimensional elements. It appears as the vertices in all higher polytopes.

Point
(OFF file)
Rank	0
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Point
Coxeter diagram
Elements
Vertex figure	Nullitope
Measures (edge length 1)
Central density	1
Number of external pieces	1
Level of complexity	1
Related polytopes
Army	Point
Dual	Point
Conjugate	None
Abstract & topological properties
Flag count	1
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A0, order 1
Convex	Yes
Nature	Tame

A point is simultaneously a 0-simplex, a 0-hypercube, and a 0-orthoplex. Furthermore, a point is the pyramid of the nullitope.

Somewhat contrary to intuition, the point is technically asymmetrical, as its only automorphism is trivial.

Vertex coordinates

Coordinates for a point are simply:

• $()$.

External links

• Bowers, Jonathan. "Zero Dimensional Shapes".

• Wikipedia Contributors. "Point (geometry)".