A circular walk
| The following picture is a stereogram picture pair of the smallest non-trivial generalized quadrangle (cross your eyes to see it in 3d). This geometry and its various highly symmetric models play an important role in the picturebook. The name `quadrangle' derives from the fact that 4 is the smallest number n for which it is possible to draw an n-gon using only lines in this geometry. |
A circular walk
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This animated GIF shows a (red) circular walk on my favourite plane model of the smallest non-trivial generalized quadrangle which visits every point and every line exactly once. The model itself, that is, the union of the red and purple picture in the middle of the animation, is called the doily. The 15 lines in this model are the 5 edges, the 5 diameters and the 5 circle segments inscribed in the pentagon. |
| Here a stereoscopic animation of the spatial model of the generalized quadrangle of order (2,2) (large, still not quite what I want). | Here you will find a stereoscopic animation of a spatial model of the generalized quadrangle of order (4,2) (very large and, again, still needs some work). |