#tutorial

It is Baldequin (or Baldachin) in English, Baldeken, or Baldöken in Turkish. I don’t know which one is correct, but it is the name of a structural system of arches and pendentives that carry a dome. Sinan experimented with square, hexagonal, and octagonal variations in his mosque designs (as I developed parametric definitions of them in my 2003 master thesis (here)). Today, together with students we’ve modeled the system and tried to generate some variations by manipulating its parameters. Below…

I learned this method from the open math resources website. I couldn’t help myself repeat it in Rhinoceros. It was quite fun to solve circle tangency problems in 2D, this is one of them: drawing the circle that passes three given points, not using ready-made commands but only geometric tools of the circle (compass) and ruler (line). Here is the sequence of it: First of all, we need to know that the circle we are looking for is centered somewhere…

Becoming popular after the Beijing 2008 Olympics National Aquatics Centre‘s facade (which is believed to be a Voronoi subdivision, as an epic mistake), the Weaire Phelan structure is a solution of equal volumes with minimal surface area. This nice website briefly explains the phenomenon. There is also an implementation on Grasshopper by Jon Mirtschin. Here, I will be modeling the Tetrakaidecahedron of the Weaire-Phelan structure. First, we define the overall size by drawing a 20×10 rhombus. Copy the rhombus by…

Yes, Revit revolutionizes the design process if you get used to it’s interface; but there are lots of things that could be further developed. Representational qualities, for example seems to be an important issue. I use section-perspectives a lot but still there are anti-aliasing problems when you get to the printing process. The last project I developed bottom-up in Revit and printed the posters from it, without any photoshop. This led me to think about it’s representational capabilities. I wanted…

The Truncated Icosahedron (5,6,6) is an Archimedean Solid we often recognize as the iconic soccer ball. This geometric structure, also affectionately known as the “Buckyball” in honor of the visionary architect Buckminster Fuller, has gained significant popularity and recognition both within the realms of mathematics and everyday life. It is composed of twelve regular pentagons and twenty regular hexagons, meticulously arranged to achieve a harmonious balance. This symmetrical nature makes it a fascinating object of study in geometry and various…

The tetrahedron is a popular platonic solid for designers. We’ve explained how to draw them using equilateral triangles here before. Recently I’ve found (sorry, lost the web address) a much quicker way of modeling a Tetrahedron using a cube. It’s very simple, just connecting the three opposite corners of the cube automatically makes them equal, resulting in the four equal faces. Of course this time you’ll have to calculate the actual edge length, but if you use the “box diagonal”…

In this experiment, I’m trying to use data recorder to change components on a surface. The component part is a standart triangular construction, but the attractor points are defined by a 2D slider that is connected to a data recorder. Data recorder remembers last 15 points, while you move the 2d slider, last 15 points are projected on the base surface. This creates an illusion as if a “snake” game on a surface. Definition then uses the closes point distance…

Since the mid-20th century, the hyperbolic paraboloid surface has been one of the most popular mathematical forms for architects. Named Hypar in short, this is the Quadric Surface equation of the Hyperbolic Paraboloid. Erik Demaine summarizes several examples from architecture such as the roof of the Girls’ Grammar School in London (designed by Chamberlin, Powell, and Bonn), the Philips pavilion at the 1958 Brussels exhibition designed by Le Corbusier, and finally, Frei Otto illustrated and analyzed a grid of connecting…

An octahedron is a polyhedron and platonic solid with 8 faces of identical equilateral triangles. In this post, I will try to explain the drawing and unrolling process of the octahedron. It has a close relationship with the cube as it’s dual. In order to construct an octahedron, we first have to create a square. The main problem of drawing the square is determining the right angle (perpendicular axis) to any point in Euclidean space. We’ll draw it here as…

The dodecahedron is a Platonic Solid with 12 equilateral pentagonal faces. It has a close relationship with its 20-sided dual, Icosahedron. Mete Tüneri showed the following method of Dodecahedron construction, using only distances, corners of the pentagon, and a visionary equilateral triangle underneath. We’ll construct Dodecahedron, assuming that we’ve drawn an initial equilateral pentagon. We need to find out the pentagon’s angle of 3d rotation. First, put spheres at points a and c, with a radius of a to c. The…