Perfect Parallelepiped

thingiverse

This is a 3D model of a Perfect Parallelepiped. A parallelepiped is a three-dimensional shape formed by six parallelograms. (A cube is a specific kind of parallelepiped where all six faces are perfect squares). A Perfect Parallelepiped is one where each edge length, the diagonal length on each face, and the diagonal lengths between opposite corners are all positive integers. Or phrased differently, a box where the length between any two 'corners' of the box is a whole number. One was finally found in 2009! This is an OpenSCAD file that generates the Perfect Parallelepiped described in the paper "Perfect Parallelepipeds Exist". (1) The sides are 271, 106, and 103mm in length. The minor face diagonal lengths are 101, 266, and 255mm. The major face diagonal lengths are 183, 312, and 323mm. Lastly, the body diagonal lengths are 374, 300, 278, and 272mm. Printing at 25% scale yields a nice hand-held size. (1) J. Sawyer and C. Reiter, "Perfect Parallelepipeds Exist," arXiv:0907.0220v2 [math.NT], 15 Dec 2009