They could need three dimensional space. Although points are 1-dimensional objects, it is easy to have four points that need 3-d space: for example the vertices of a tetrahedron (triangular pyramid). Similarly, skew line will need 3-d space.
The surface of a sphere is defined in that manner.
This is the definition of a line segment. They are used in constructing two-dimensional polygons.
In that case, it wouldn't be called a "line".From superscot85: No, all lines are one-dimensional, just as all points are zero-dimensional.
That is called a sphere.
Two dimensional geometry.
Points with integer coordinates are often called lattice points. Lattices exist in all dimensions.When we talk about lattices points on the rectangular Cartesian coordinate system, this is a two dimensional lattice. Three dimensional lattice points are often used to study crystals.
On a sphere, all points on the surface are equidistant from the center.
The three dimensional figures are called Space figures
All three dimensional figures have more faces than a one dimensional figure. There are an infinite number of one dimensional points on a three dimensional figure
If the shape is two-dimensional then it is a circle, if the shape is three-dimensional then it's a sphere.
A 'spherical' surface.
Points are the only such objects.