Point

Point
Rank0
TypeRegular
SpaceSpherical
Notation
Bowers style acronymPoint
Coxeter diagram
Elements
Vertex figureNullitope
Measures (edge length 1)
Central density1
Number of pieces1
Level of complexity1
Related polytopes
ArmyPoint
DualPoint
ConjugateNone
Abstract properties
Flag count1
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryA0, order 1
ConvexYes
NatureTame
Discovered by{{{discoverer}}}

The point (also called monad or monon[1]). 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.

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:

• ${\displaystyle ()}$.