The geometric figures are both solutions to the following problem: on a regular two-dimensional plane, place segments of equal length such that each segment touches three others at the vertices. Attempt to do this with as few segments as possible. Optionally, these segments should not cross. For non-crossing, our solution uses 120 segments. The best solution (to our knowledge) for non-crossing uses 104 segments. Our solution with crossing uses 48 segments. Both our solutions have 12 axes of symmetry. Note that in the animated gif the two figures are slightly not to scale for aesthetic reasons, otherwise they would fit into each other.

The animated gif is Copyright by Sebastian S. Szyszkowicz, 2008.