How different numbers of objects can be arranged in space

Represent any object by a small sphere.

Two objects define a Line.

Three objects can define a Line or define an Area.

Four objects can define a Line, define an Area or define a Volume

Five objects can define a Line, define an Area or define a Volume

Is there a 4-dimensional arrangement?  I suspect ‘yes’.

This is the best 2-dimensional projection of it I can draw.

It seems that an arrangement of n objects can occupy a maximum of n - 1 dimensions.