Geometry is the base class. It is an abstract class. The instantiable
subclasses of Geometry are restricted to zero-, one-, and
two-dimensional geometric objects that exist in two-dimensional
coordinate space. All instantiable geometry classes are defined so that
valid instances of a geometry class are topologically closed (that is,
all defined geometries include their boundary).

The base Geometry class has subclasses for Point, Curve, Surface, and
GeometryCollection:

o Point represents zero-dimensional objects.

o Curve represents one-dimensional objects, and has subclass
  LineString, with sub-subclasses Line and LinearRing.

o Surface is designed for two-dimensional objects and has subclass
  Polygon.

o GeometryCollection has specialized zero-, one-, and two-dimensional
  collection classes named MultiPoint, MultiLineString, and
  MultiPolygon for modeling geometries corresponding to collections of
  Points, LineStrings, and Polygons, respectively. MultiCurve and
  MultiSurface are introduced as abstract superclasses that generalize
  the collection interfaces to handle Curves and Surfaces.

Geometry, Curve, Surface, MultiCurve, and MultiSurface are defined as
non-instantiable classes. They define a common set of methods for their
subclasses and are included for extensibility.

Point, LineString, Polygon, GeometryCollection, MultiPoint,
MultiLineString, and MultiPolygon are instantiable classes.

URL: http://dev.mysql.com/doc/refman/5.1/en/gis-geometry-class-hierarchy.html

