Here I’ve come across to a nice website about the short history of tilings and tessellations: http://gruze.org/tilings/. I’m especially interested in the role of Albrecht Dürer, who seem to pioneer some of the concepts of today’s emerging field of architectural geometry. In this website Kevin Jardine explains mathematical aspects of some of the ancient tilings in a very understandable format. Here is a phrase from his section about Dürer; Like Kepler, Dürer was fascinated with regular polygons and polyhedra, although more for their practical visual possibilities than as the basis for mathematical […]

In Turkish there is a strange word “baklava” that has many uses. According to wikipedia: Baklava is a rich, sweet pastry made of layers of filo pastry filled with chopped nuts and sweetened with syrup or honey. It is characteristic of the cuisines of the former Ottoman Empire and those of Central and Southwest Asia. However we should add that 150 gr. of baklava is 413 calorie. Here is it (with pistachio): The other use of this word comes from the shape of baklava slices. They are always cut in […]

This is a small exercise, to remember old-school tessellation of surfaces. While reading about rhombic dodecahedron (the stackable solid), I’ve come by this tiling. It’s quite simple, just a hexagonal grid, animated by a variation of Breststroke surface function (described here), then reconstructed as three quadrangles with proper vertex id. [GHX: 0.9.0006] here is the Grasshopper definition. You may subdivide any surface to create such tessellations, this time I chose to rebuild the surface from hexagonal cells.