Welcome

How to…

fly the spaceship

retract the walls

change the space

choose the content

centerpiece

color coding

Clifford parallels

vertex figures

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.

content preference

# Vertex Figures

When you make a finite universe from a polyhedron, the polyhedron’s corners come together with their own particular symmetry. For example, if you go to the File menu, choose Open…, navigate to the Basic folder, and select the 3-Torus, you’ll see that while the 3-torus is made from a cube, the corners come together with octahedral symmetry.

To see the vertex figures clearly, use the left ( ← ) and right ( → ) arrow keys to open the walls almost all the way, so only very thin strips remain. That way you can see the whole vertex figure at once, without the walls getting in the way.