A geometric polygon is a shape or model that covers all X, Y and Z coordinates, this means the shape or model will have: vertices, edges and faces. NURBS and polygonal models are the two main geometric theories used in 3D modelling.
NURBS surfaces:
These are created by the software generating a smooth face joining two or more curves, these curves are very accurate and therefore used in the development of automotive design and also engineering. 
Polygonal models:
This form of modelling is created with vertices, edges and faces, It is mainly used in games, film and animation, this is because these models are easy to manipulate and have a high quality end result.
Meshes:
A mesh is is what makes the model, when all the vertices, edges and faces are joined up a mesh is formed, the mesh is a surface created by joining these three up.
Vertices:
Vertices (plural of a vertex) are practically the corner of a shape or surface, at this point a coordinate is given to later plot and be joined by edges and faces creating a shape.
Edges:
These are used to join vertices together, once these has been added the skeleton of the model is made.
Faces:
Finally faces are what turn a skeleton model to an actual model, these join the edges together and they can have their colour or transparency changes to suit the models design or function.
The Cartesian co-ordinate system works using the X, Y and Z axis, it allows 3D models to be created by giving each vertex a 3D co-ordinate as shows in the image below.
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