
Journal for Geometry and Graphics 12 (2008), No. 2, 133140 Copyright Heldermann Verlag 2008 Metrics in ThreeDimensional Lattices Casey Mann Dept. of Mathematics, University of Texas, 3900 University Boulevard, Tyler, TX 75799, U.S.A. cmann@uttyler.edu Ben McCarty Dept. of Mathematics, University of Texas, 3900 University Boulevard, Tyler, TX 75799, U.S.A. Jennifer McLoudMann Dept. of Mathematics, University of Texas, 3900 University Boulevard, Tyler, TX 75799, U.S.A. jmcloud@uttyler.edu Ramona Ranalli Dept. of Mathematics, University of Texas, 3900 University Boulevard, Tyler, TX 75799, U.S.A. Nathan Smith Dept. of Mathematics, University of Texas, 3900 University Boulevard, Tyler, TX 75799, U.S.A. nathan@math.uttyl.edu We find formulas for metrics on threedimensional point lattices which count the number of steps required connect a given lattice point to the origin. Such formulas are previously known for the simple cubic lattice and the facecentered cubic lattice. We provide analogous formulas for the simple hexagonal lattice and the bodycentered cubic lattice. Keywords: Point lattices, metrics. MSC: 52C07 [ Fulltextpdf (130 KB)] for subscribers only. 