Definition:Geometric Figure

Definition
A geometric figure is intuitively defined as a set of points and lines in space.

As defined by Euclid:


 * "A figure is that which is contained by any boundary or boundaries."

The boundary may or may not be included in a particular figure. If this is important (and in the study of topology it usually is), then whether it is included or not needs to be specified.

Plane Figure
A plane figure is a geometric figure embedded in the plane.

Three-Dimensional Figure
A three-dimensional figure is a geometric figure which can not be embedded in the plane, but which can be embedded in three-dimensional space.

A common term for this is solid figure but this is a misnomer as it is usual to be studying the surfaces of such figures, which themselves are not solid as such.

Rectilineal Figure
As Euclid defined it:


 * "Rectilineal figures are those which are contained by straight lines."

The usual name for a plane rectilineal figure is polygon.

The usual name for a 3-dimensional rectilineal figure is polyhedron.

Diameter
The diameter of a geometric figure is the greatest length that can be formed between two opposite parallel straight lines that can be drawn tangent to its boundary.

Compare with the diameter of a circle, whose definition is consistent with this.

Note
The diameter of a parallelogram is not consistent with this definition.