A geometry video is formed as a sequence of geometry images where each frame is a remeshed form of a frame of an animated mesh sequence. For efficiently coding geometry videos by exploiting temporal as well spatial correlation at multiple scales, this paper proposes the 3D-SPECK algorithm which has been successfully applied to the coding of volumetric medical image data and hyperspectral image data in the past. The paper also puts forward several postprocessing operations on the reconstructed surfaces that compensate for the visual artifacts appearing in the form of undulations due to the loss of high-frequency wavelet coefficients, cracks near geometry image boundaries due to vertex coordinate quantization errors and serrations due to regular or quad splitting triangulation of local regions of large anisotropic geometric stretch. Experimental results on several animated mesh sequences demonstrate the superiority of the subjective and objective coding performances of the newly proposed approach to those of the commonly recognized animated mesh sequence coding approaches at low and medium coding rates.