Dürer Rhombii
I’ve come across this nice website about the short history of tilings and tessellations. In this post, I am regenerating a tiling of Dürer rhombii. Albrecht Dürer sounds like one of the pioneers of some of the concepts of today’s emerging field of architectural geometry. Here is a phrase from that website about Dürer;
“…Like Kepler, regular polygons and polyhedra fascinated Dürer… A large section of the Painter’s Manual is dedicated to practical ways to construct various curves and regular polygons with a ruler and compass. Kepler goes over some of the same ground in the first book of Harmonices Mundi but only includes mathematically exact constructions. The more pragmatic Dürer also includes approximations, including one for the regular heptagon. (One can prove that there is no exact construction using a ruler and compass for this shape.)…”
“…Dürer was one of the first people to provide flat paper models folded into polyhedra. He provides more than a dozen examples… The Painter’s Manual also includes a brief section on polygon tilings. Dürer illustrates the three regular tilings consisting respectively of squares, triangles, and hexagons, as well as the 4.8.8 octagon tiling and the 3.6.3.6 uniform tiling with its striking six-pointed star pattern. He also shows examples of non-edge-to-edge tilings with triangles and squares..”
Here I developed Grasshopper code for one of the rhombic tilings from that website. I like these tilings. Because they open new variations to the seemingly limited area of tessellations;
Here is the Grasshopper definition file for Dürer Rhombii:
Cite this post
Related Posts
Space-filling Rhombic Dodecahedra
February 10, 2024
The rhombic dodecahedron is a polyhedron with twelve rhombus-shaped faces, where each face has four sides of equal length. It is possible to construct the space-filling variant of the rhombic dodecahedron by arranging multiple such rhombic dodecahedra in a regular pattern so that they fill space without leaving any gaps. In his 1611 work on snowflakes titled “Strena seu de Nive Sexangula,” Johannes Kepler observed that honey bees utilize the geometric structure of rhombic dodecahedra to construct honeycombs. These honeycombs…
Rhombille Tiling on Surface
June 13, 2023
This is an update on my 2012 exercise on rhombille tiling. This reminded me of the old-school subdivisions of surfaces again after 11 years. It was while reading about rhombic dodecahedron (the stackable solid), that I came across this cute tiling. It’s quite simple, just a hexagonal grid with a special reconstruction. I decided to recreate it by using well-known native Grasshopper components. I animated the result with a variation of the Breaststroke surface function (described here). Then I reconstructed…
Rhombus Facade
June 4, 2023
This is the continuation of a very old parametric model of a building facade, presented here. I will introduce the basic Grasshopper definitions of several alternative designs. The first one is the rhombus facade. The first part of the algorithm deals with the necessary data collection. We reference a polyline from the Rhino model as the path that the facade will follow. After that, we create vertical lines around the path. Then, we shatter these lines by using a Graph…
Albrecht Dürer
July 22, 2013
In the 14th century, Albrecht Dürer basically seems to capture some of the fundamentals of contemporary parametric design. Apart from other thinkers of his age, he refused to accept one single definition of beauty, based on proportions. His famous physiognomical studies reflected very early examples of referential systems that generate diverse design outputs, even a half-century before Descartes published the coordinate system and four centuries before D’Arcy draw the formal studies on species. I don’t know if he is mentioned…
Baklava
January 23, 2013
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 calories. Here is it (with pistachio): The other use of this word comes from…