Welcome

How to…

fly the spaceship

retract the walls

change the space

advanced

choose the content

export the image

set your preferences

Further study

Acknowledgments

Still have a question? Submit it to the Geometry Games Contact Page for a more-or-less prompt reply.

Curved Spaces is freely distributable under the GNU General Public License. The current version is available at www.geometrygames.org/ CurvedSpaces.

# 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 3-torus,
- the Poincarédodecahedral space, and
- the mirrored right-angled dodecahedron.

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 File ▸ 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.