Abstract: Polyhedral mesh simplification with additional properties (such as color, texture etc.) is often used in computer visualization, computer simulation, mesh transmission etc. Instead of 3-dimensional vector, the algorithm uses n-dimensional vector, which contains the information of coordinates, colors, textures etc, to describe the mesh vertex. Symmetric Hausdorff distance in Rn space is used to control the error of simplification. The algorithm successfully preserves the color and texture appearance of the original data field and guarantees that the simplified mesh matches well with the original one.