How to create your own space
(for 3-manifold experts)

You aren’t limited to the built-in Sample Spaces. To make your own space, create a plain text file containing a list of 4×4 matrices generating the space’s group of covering transformations. See, for example, the built-in files for

The matrices belong to the group O(4) for spherical spaces, O(3,1) for hyperbolic spaces (with the timelike component last), and the analogous group for flat spaces.

Curved Spaces uses the (row vector)(matrix) convention rather than the (matrix)(column vector) convention, so the matrices may be the transposes of what you were expecting. In the spherical case this makes no difference because the transpose equals the inverse, but in the flat and hyperbolic cases it’s important to get it right.

Let your text editor save your 4×4 matrices as a plain .txt file, then manually change the filename extension to .gen.
Macintosh: This assigns the Curved Spaces icon, which you may double-click to open the file in Curved Spaces.
Windows: To open the file, choose Open from within Curved Spaces.

Curved Spaces 3.0 includes a smaller, more streamlined library than Curved Spaces 1.0 had. The omitted spaces are available upon request.