Modeling Cylinder Hypar

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…

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 the basic drawing and modeling commands of the Rhinoceros software. Here, I use the point surface command. Because, in Rhinoceros, generally we describe the parametric surfaces as four-sided objects. So, this exercise is a basic…

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, you can see them often in art, design, and mathematics. In this short video tutorial, I am modeling truchet relief in Rhinoceros CAD software. My purpose of this modeling process is to demonstrate the basic…

In art, design, and geometry, folding involves bending or creasing a material, such as paper, fabric, or other flexible materials into defined shapes or patterns. In this short tutorial video, I am modeling a folds relief pattern. This pattern stands out due to its resemblance to a collapsible folding system, combining both structural and aesthetic qualities. We refer to it as a folds relief pattern because it also mimics a relief design, creating light and shadow effects. This video series…

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 irregular truncated icosidodecahedron. It is not the regular Archimedean solid, but a rough approximation of it. I made this model to exercise the exploration of new polyhedra by using rectification and truncation operations. Nevertheless, here…