The representation of geographic objects is most naturally supported with vectors. After all, objects are identified by the parameters of location, shape, size and orientation, and many of these parameters can be expressed in terms of vectors. We can define features within the topological space that are easy to handle and that can be used as representations of geographic objects. These features are called simplices as they are the simplest geometric shapes of some dimension: point (0-simplex), line segment (1-simplex), triangle (2-simplex), and tetrahedron (3-simplex). When we combine various simplices into a single feature, we obtain a simplicial complex. When area objects are stored using a vector approach, the usual technique is to apply a boundary model. This means that each area feature is represented by some arc/node structure that determines a polygon as the area’s boundary. A polygon representation for an area object is another example of a finite approximation of a phenomenon that may have a curvilinear boundary in reality. In images, the shape of objects often helps us to identify them (built-up areas, roads and railroads, agricultural fields, etc.).