  The present paper suggests a new approach for geometric representation of 3D
spatial models and provides a new compression algorithm for 3D meshes, which is
based on mathematical theory of convex geometry. In our approach we represent a
3D convex polyhedron by means of planes, containing only its faces. This allows
not to consider topological aspects of the problem (connectivity information
among vertices and edges) since by means of the planes we construct the
polyhedron uniquely. Due to the fact that the topological data is ignored this
representation provides high degree of compression. Also planes based
representation provides a compression of geometrical data because most of the
faces of the polyhedron are not triangles but polygons with more than three
vertices.
