Journal for Geometry and Graphics 12 (2008), No. 2, 133--140
Copyright Heldermann Verlag 2008
Metrics in Three-Dimensional 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 McLoud-Mann
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 three-dimensional 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 face-centered cubic lattice. We provide analogous formulas for the simple hexagonal lattice and the body-centered cubic lattice.
Keywords: Point lattices, metrics.
MSC: 52C07
[ Fulltext-pdf (130 KB)] for subscribers only.