This paper describes the construction of second generation bandelet bases and their application to 3D geometry compression. This new coding scheme is orthogonal and the corresponding basis functions are regular. In our method, surfaces are decomposed in a bandelet basis with a fast bandeletization algorithm that removes the geo- metric redundancy of orthogonal wavelet coefficients. The result- ing transform coding scheme has an error decay that is asymptoti- cally optimal for geometrically regular surfaces. We then use these bandelet bases to perform geometry image and normal map com- pression. Numerical tests show that for complex surfaces bandelets bring an improvement of 1.5dB to 2dB over state of the art com- pression schemes.