Truncated Icosahedron (5,6,6) is an Archimedian Solid, probably the most popular one because of it’s apperance as the soccer ball. It’s constructed by trimming one third of each edge of an Icosahedron, (a Platonic Solid described here). In order to find 1/3’s of each edge, I used duplicate border, explode and divide commands to get the points that construct the pentagons and hexagons, while paneling is done by using planar surface commands on closed polyline edges. (If you are interested in how we reached the initial solid, refer to the […]

## icosahedron

I have come across several highschool topics I was afraid of. While I was searching for a geodesic dome definition in Grasshopper, it was quite surprising that I found an easier way of modeling an approximation of icosahedron, the famous platonic solid. Icosahedron was a research topic of this website at various posts before (here, here and here). In order to generate geodesic spheres, first I had to solve icosahedron. My first experiment was partially successfull. I knew, icosahedron’s points lie at regular pentagons which are pulled onto a sphere. […]

Not all of them, but when you get the idea, you’ll see there are lots of different alternatives in creating Fuller’s famous Geodesic Domes (Although in fact, he is not the inventor of it). I was playing with Platonic Solids in Rhino, and realized that “Pull” command is very useful in subdividing objects. Taking a regular Icosahedron (which is the most popular Geodesic dome starter), and dividing it, as Fuller’s notation, Class I-2V. This is the simplest form of a Geodesic subdivision, creating two kinds of struts (not all of […]

I tried different approaches to draw platonic solids using Grasshopper’s native components. However, it seems impossible now. In geometric definition, platonic solid is a set of points, distributed on a sphere with equal distances. If the set contains 12 points, then it’s an icosahedron. I found lots of information about these objects and mathematicians seem to love analyzing them. They created different approaches to build an icosahedron. One of them is very suitable to implement on Grasshopper’s VB component. They defined exact relative coordinates of each point. This was a […]

Dodecahedron is a Platonic Solid with 12 equilateral pentagonal faces. It has a close relationship with it’s 20-sided dual, Icosahedron. Mete Tüneri showed the following method of Dodecahedron construction, using only distances, corners of pentagon and a visionay 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 the radius of a to c. Intersection of these spheres result a circle. We know that, every point on […]

Icosidodecahedron is an Archimedian Solid, a thing in between the Platonic Solids of Icosahedron (d20) and Dodecahedron (d12). It is a rectified version of Icosahedron, constructed with dividing every edge of it into two equal segments, and joining these segments to create a composition of equilateral pentagons and triangles. Archimedian Solids consists of at least two equilateral polygons, whereas Platonic Solids are constructed by only one. We’ll deduce an Icosidodecahedron from Icosahedron below; First, you should create an Icosahedron, the Platonic father of Icosidodecaheron. After that, all faces should be […]

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 […]