Exploring dual polyhedra in Grasshopper is an interesting topic. In this post, I try to generate the dual of any polyhedron using Rhino Python and possibly Grasshopper. I developed this code for Rhino Python earlier here, and now I have converted it into a Grasshopper-Python…

String art is a captivating technique that combines geometry and aesthetics to recreate images using lines between pins. Here is a good reference to start studying it. In this post, I explored a custom Rhino Python script designed for Rhinoceros 7 and 8. It transforms…

Differential growth is a process where different parts of a structure grow at different rates, leading to complex forms. After watching this, I decided to try it in Grasshopper. Here, differential growth mimics this behavior by applying rules such as Repulsion to avoid crowding or…

An aperiodic tiling is a pattern that covers the plane without ever repeating itself (i.e., it is non-periodic). A few special shapes, arranged according to specific rules, can cover the entire plane, but the resulting pattern never repeats exactly. I challenged myself on a 3-day…

The Fourier Transform is a powerful mathematical technique that allows us to analyze the different frequency components within a signal or shape. Its discrete version, the Discrete Fourier Transform (DFT), is used when working with numerical data. I studied the Fourier Series here before. One…

In large-scale projects, calculating tiling layouts for wall, floor, and ceiling surfaces becomes even more critical. Evolutionary optimization of these tilings seemed to be a viable approach yesterday. Considering how time-consuming and labor-intensive this process can be, I tried using Galapagos, an old but often…

Although it appears simple, Goldberg Polyhedra in Grasshopper became a tough challenge, which I like a lot. I spent about 24 hours attempting to generate these polyhedra. I started with Goldberg’s original method. This creates an equilateral triangle using coordinates denoted as m and n…

The Hilbert Curve is one of the results of David Hilbert’s vision of mathematics as a network of symbolic systems. Defined in 1891, this curve is a fractal that fills a two-dimensional plane with a one-dimensional line in the limit. It exhibits self-similarity. It emerged…

I had been researching Goldberg Polyhedra for a while. While exploring how to perform chamfer operations in Grasshopper, I found some interesting results. I want to share them with you. In this Grasshopper project, I reused my previous work, where I built a dodecahedron using…

Robotic EarthCrafts II occurred in the summer of 2024 at Istanbul Bilgi University, seven years after the first. Together with Fulya Özsel Akipek, Nilüfer Kozikoglu, Abdullah Mallah, and Halit Mallah, we experimented with the robotic fabrication of molds for rammed-earth structures. The focus shifted toward a human scale based on…

3D printing, also known as additive manufacturing, is a process of creating three-dimensional objects from a digital file by building them layer by layer. Unlike traditional manufacturing, where the material is cut or molded into shape, 3D printing adds material in successive layers. This allows…

Relief in the context of art and sculpture refers to a technique where a three-dimensional form is created on a flat surface. The object or figure “protrudes” from the background, creating depth and texture. In this short tutorial video, I am modeling waves relief using…

Truchet patterns refer to a set of geometric designs based on simple, repeating shapes, usually tiles or squares. These tiles can be rotated or flipped to create complex and visually interesting patterns. A French mathematician, Michel Truchet introduced these patterns in the 1970s. Since then,…

A “hypar” is short for a hyperbolic paraboloid, a double-curved, saddle-shaped surface often used in architecture and structural design due to its unique geometric properties. It is a ruled surface, meaning it can be constructed entirely with straight lines, despite its curved appearance. In this…

In art, design, and geometry, folding involves bending or creasing a material—such as paper, fabric, or other flexible substances—into defined shapes or patterns. Folding techniques can also be used to create multidimensional forms and structures, blending artistic expression with practical functionality. In this short tutorial…

In geometry, a truncated icosidodecahedron, rhombitruncated icosidodecahedron, great rhombicosidodecahedron, omnitruncated dodecahedron, or omnitruncated icosahedron is an Archimedean solid. It is one of thirteen convex, isogonal, non-prismatic solids constructed by two or more types of regular polygon faces. In this short tutorial, I am constructing an…

The sphenoid hendecahedron is a unique and interesting polyhedron. As the name implies, a “hendecahedron” is a polyhedron with 11 faces, while “sphenoid” refers to a specific type of shape that is often unusual, asymmetrical, and typically wedge-shaped. This polyhedron fills space, packing 3D space…