Point

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Point
Rank0
TypeRegular
Notation
Bowers style acronymPoint
Coxeter diagram
Elements
Vertex figureNullitope
Measures
Central density1
Number of external pieces1
Level of complexity1
Related polytopes
ArmyPoint
DualPoint
ConjugateNone
Abstract & topological properties
Flag count1
Euler characteristic0
OrientableYes
Properties
SymmetryA0, order 1
Flag orbits1
ConvexYes
NatureTame

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[edit | edit source]

Coordinates for a point are simply:

  • .

References[edit | edit source]

External links[edit | edit source]