Welcome

How to…

fly the spaceship

retract the walls

change the space

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.

# Curved Spaces 3

Curved Spaces is a flight simulator for finite universe models (“3‑manifolds”) or, if you prefer, for tilings of 3-dimensional spherical, flat and hyperbolic spaces. To get started, please choose the page How to fly the spaceship from the index on the left.

The view inside a hyperbolic dodecahedron with mirrored walls and all right angles. A single galaxy sits at the dodecahedron’s center. Alternatively, you may equally well interpret this picture as a tiling of 3-dimensional hyperbolic space by an infinite number of identical right-angled dodecahedra. Either way, the image is somewhat atypical: most of the Sample Spaces that come with this package represent universes that “wrap around” and connect up with themselves without reflection.