Icosahedron is one of the five Platonic Solids with twenty equilateral triangular faces. It’s dual is Dodecahedron, which has pentagonal faces. Here, Icosahedron is constructed by using pentagons. Interesting thing is it’s close relationship with Dodecahedron, although they seem to be very different. This time we won’t lose time with two dimensional pentagon drawing. Maybe we’ll discuss that later. Assuming you’ve created a regular pentagon, you should find the “tip” point of the Icosahedron by intersecting spheres from at least three of the corner points with a radius of pentagon’s […]


Truncated Tetrahedron is an Archimedian Solid, created by slicing a Tetrahedron. It’s faces are regular hexagons and triangles. Assuming you’ve created a Tetrahedron, first join it’s faces to create a polysurface. Now, you may re-create the lines of Tetrahedron’s edges, either by drawing them or generating them (Curve/Curve from Objects/Duplicate Edge). While the edge lines are selected, hit (Curve/Point Object/Divide Curve By/Number of Segments) and type 3 to the number of segments to be created. Now all edges should be divided equally into three parts. Draw the equilateral triangles, connecting the […]


This is a semi-regular tessellation of vertex arrangement 4.8.8. It’s octagonal and square forms are all generated from data lists provided by new version of subdivide component (Old one was processing points in a different fashion. I don’t know why they changed that). Anyway, a lexical operation is needed to convert this list into a more useful for this exercise. You can download the source definition here [2011_12_25_srtessela]. However you need to define a surface in order to start it. The component labeled with “pattern” is actually the data list […]


Tetrahedron is a platonic solid with 4 equal triangular faces (which are also equilateral), 6 equal edges and 4 vertices. While creating this shape, we will take a closer look at length transfers using compass-like tools both in two and three dimensional space. In order to define the edge length of first triangle (which is a straight line), start with any two points in cartesian space. Using compass (arc or circle), draw two arches (or circles) using your initial points as corners, and the distance between your points as radius. […]


Since the “Sine Surface” has become vey popular, it’s best used in educational settings where quick and effective parametric surfaces are needed. However, I tried to further develop this idea to create not only the sine edge surface, but also a surface that can be mapped by any graph function. The definition found here [2011_12_22_sine]does calculate points according to a graph output, but does not create edge surface yet. Here is an updated version of this project Update: Here is an updated version of this Grasshopper definition: [GHX: 0.9.0072]


“There are three fundamental properties of organization in a computer that are very different from the characteristics of inert mediums such as paper and pencil: topology, time, and parameters. These three properties should be discussed, beginning with the principles of topological entities, continuing with the implications that topological forms raise for the relationship between time and shape, and concluding with a discussion of statistics and parameters that can be stored in these timed surfaces.” “The concept of an envelope of potentials either a single or a series of instances can be taken, is radically […]


Scripting languages have become one of the main environments of generative design since beginning of the new millenium. Also as a new research field, design researchers focused on the potentials of this medium. However this has caused a field dependency to computer programming, as scripting could not be conceptualized by design researchers independent from computer programming paradigms. This leads designers to conflicts of cognitive duality and potential pedagogical misleads. Recent studies in computer programming showed that procedural coding, based on the flow of control has a user friendly alternative. Since […]


One of the main concepts of a contemporary design geometry studies include “emergent geometries”. We used to ask students explore new shapes out of complex or ruled compositions. Here is a definition in Grasshopper3d to simulate a perceptual process of discovering polygons with selected number of edges within a regular array of shape compositions. The definition can be downloaded here [2011-11-14_emergent]