For a combinatorics problem, I need point sets of 100 to 1000 3D points, with the restriction that generation is 1 line of code. For example:
Tuples[Range[-3, 3], {3}]
Select[Tuples[Range[30], {3}], IntegerQ[Norm[#]] &]
Select[Tuples[Range[-7, 7], {3}], BitXor @@ Abs[#] == 0 &]
You can use the code of your choice, but no fetching data from elsewhere is allowed. What are some really nice 3D point sets? Here's a nice set of points where the code is too long.
base = {{0, 0, 0}, {180, 180, 180}, {252, 252, -252}, {420, 420, 420}, {1260, 1260, -1260}, {0, 0, 420}, {0, 0, 1260}, {0, 180, 360}, {0, 315, 315}, {0, 360, 180}, {0, 420, 840}, {0, 630, 630}, {0, 840, 420}, {140, 140, 420}, {180, 180, -540}, {252, 252,756}, {420, 420, -1260}};
tetrahedral[{a_, b_, c_}] := Union[{{a, b, c}, {a, -b, -c}, {b, c, a}, {b, -c, -a}, {c, a, b}, {c, -a, -b}, {-c, a, -b}, {-c, -a, b}, {-b, c, -a}, {-b, -c, a}, {-a, b, -c}, {-a, -b, c}}];
points = Union[Flatten[tetrahedral[#] & /@ base, 1]];
The 149 points make 241 lines of 5 points, that's kinda interesting. Is it possible to get more interesting with less code?
If you are interested in thinking of points as vertices of a graph embedding then you have a lot of options. I personally like the symmetry of circulant graphs. For some other interesting graph families, that are pretty simple to generate, you could look at random spanning trees, regular graphs, graphs of certain images, etc. below is some Mathematica code for generating a random circulant graph with edge density parameterized by k