making a fast projection of a crytsallographic unit cell

*To*: mathgroup at smc.vnet.net*Subject*: [mg80779] making a fast projection of a crytsallographic unit cell*From*: Roger Bagula <rlbagula at sbcglobal.net>*Date*: Sat, 1 Sep 2007 00:32:47 -0400 (EDT)

The problem is that I want to plot representations of crystallographic cells fast in Mathematica. The face centerd cubic unit cell can be represented in 3d as a set of points. Hermann-Mauguin space groupo notation: Fm3m Sodium Chloride and many metal crystals use this crystal cell. (* points for cubic close pack/ face centered cubic*) p = {{1, 1, 1}, {1, 0, 0}, {2, 1, 0}, {0, 0, 1}, {2, 2, 1}, {1, 2, 2}, {0, 1, 2}, {0, 1, 0}, {1, 2, 0}, {0, 2, 1}, {2, 0, 1}, { 2, 1, 2}, {1, 0, 2}}; pieces = Complement[ Flatten[Table[{i, j, k}, {i, 0, 2}, {j, 0, 2}, {k, 0, 2}], 2], p] (* showing as points*) Show[Graphics3D[Table[Point[pieces[[n]]], { n, 1, Length[pieces]}]], Boxed -> False] (* creating the equivalent of a graphic primitive like a Cuboid[] for a sphere*) Clear[sphere] << RealTime3D` (* RealTime3D allows you to drag the graphic around to see from different view points*) sphere[n_]:=ParametricPlot3D[{Sin[t]*Sin[p]/2-pieces[[n]][[ 1]],Cos[t]*Sin[p]/2-pieces[[n]][[2]],Cos[p]/2-pieces[[n]][[3]]},{t,- Pi,Pi},{p,0,Pi},Axes\[Rule]False,Boxed\[Rule]False] (* plotting them at the points them at the points*) gr=Table[sphere[n],{n,1,Length[pieces]}]; Show[gr] The problem isn't doing it, but doing it faster. There are 230 Federov space groups in 3d. Roger Bagula

**Follow-Ups**:**Re: making a fast projection of a crytsallographic unit cell***From:*Curtis Osterhoudt <cfo@lanl.gov>