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 […]
Posts with the keyword icosahedron
I have come across several high school 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 […]
Not all of them, but when you get the idea, you’ll see there are lots of different alternatives for 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 the “Pull” command is very useful in subdividing objects. I modeled this in Rhino 4. First, take a regular Icosahedron and divide it. Because, this […]
I tried different approaches to drawing platonic solids using Grasshopper’s native components. However, it seems impossible now. In geometric definition, a 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 building an icosahedron. One of […]
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 […]
Icosidodecahedron is an Archimedian Solid, a thing in between the Platonic Solids of Icosahedron (d20) and Dodecahedron (d12). It is a rectified version of an Icosahedron, constructed by dividing every edge into two equal segments and joining these segments to create a composition of equilateral pentagons and triangles. Archimedian Solids consist of at least two equilateral polygons, whereas Platonic Solids are constructed by only one. We’ll deduce an Icosidodecahedron from […]
The icosahedron is one of the five Platonic Solids with twenty equilateral triangular faces. Its dual is Dodecahedron, which has pentagonal faces. Here, I explained the construction of the Icosahedron. We won’t lose time with a two-dimensional pentagon drawing. Maybe we’ll discuss that later. So, after creating a regular pentagon, you should find the “tip” point of the Icosahedron by intersecting spheres from at least three of the corner points […]