Polygonal meshes remain the primary representation for visualization of 3D data in a wide range of industries including manufacturing, architecture, geographic information systems, medical imaging, robotics, entertainment, and military applications. Because of its widespread use, it is desirable to compress polygonal meshes stored in file servers and exchanged over computer networks to reduce storage and transmission time requirements. 3D files encoded by OBJ format are commonly used to share models due to its clear simple design. Normally each OBJ file contains a large amount of data (e.g. vertices and triangulated faces) describing the mesh surface. In this research we introduce a novel method to compress vertices and triangle faces by a new algorithm called Geometry Minimization Algorithm (GM-Algorithm). First, each vertex consists of (x, y, z) coordinates that are encoded into a single value by the GM-Algorithm. Second, triangle faces are encoded by computing the differences between two adjacent vertex locations, and then are coded by the GM-Algorithm followed by arithmetic coding compression. We tested the method on large data sets achieving higher compression ratios over 90% while keeping the same number of vertices and triangle faces as the original mesh. The decompression step is based on a Parallel Fast Matching Search Algorithm (Parallel-FMS) to recover the structure of the 3D mesh. A comparative analysis of compression ratios is provided with a number of commonly used 3D file formats such as MATLAB, VRML, OpenCTM and STL showing the advantages and effectiveness of our approach.