doily

DIY Paper Doily Winter Forest Tutorial from Oui Oui Oui Studio. All you need are wooden skewers, paper doilies or napkins and wooden beads. This is the original source so there are instructions at the link. I used Chrome to translate from French to English - but this DIY is so easy and you can scroll through the photos.

Take a set with six elements and consider all possible matchings (partitions into 2-element sets). A little thought or counting should convince you there are exactly 15 matchings. Now, we can define a peculiar incidence geometry on those set: the “points” of the geometry are these 15 matchings, and two “points” are on the same “line” precisely when they have a 2-element set in common. When you try to draw this geometry, you may end up with the symmetric configuration above, which exhibits various nice features.

The result is sometimes known as the Cremona–Richmond configuration but is more commonly referred to as the doily. In this geometry, every point is incident with three lines and vice versa (the configuration is self-dual). Moreover, the doily is triangle-free, making it the smallest non-trivial example of a generalized quadrangle.