Due to the proliferation of 3D objects, which are often expensive to manipulate in computers and to transmit across the Internet, techniques of geometric oppression are becoming increasingly important. Based on the parallelogram coordinate prediction and connectivity compression, this paper presents a near-lossless, two-pass, triangular mesh compression algorithm that achieves a compression ratio ranging from 15:1 to 40:1. An average compression ratio better than 20:1 has also been derived form a large collection of 3D objects ranging from simple man-made shapes to complex natural objects. Several derived compression algorithms, taking advantage of fold angles, have been implemented as part of the compression ratio and algorithm comparison. A linear predictive formula has been derived that effectively foretells the compression ratio from a derivable parameter of the fold-angle histogram of any given 3D-object model. The parameter x is defined as x= df/(tf- df), where df is the frequency of a dominant fold angle and tf is the total non-zero frequency. Experiments show that the predictive formula holds for most high-resolution models ($GTR1000 points). This predictability of compression ratio allows users to effectively predetermine the transmission time and the computing time requirements for any post-processing. Thus, the results presented here not only contribute algorithms for geometric compression by achieving good compression ratios but also provide valuable predictability for those dynamic or online applications.