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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.