platonic solid


Lokma is the name of a pastry made of fried dough soaked in sugar syrup or honey and cinnamon, typically shaped into a ring or ball. Unfortunately it is not the “Lokma” we’ll study here. In Turkish, there is another meaning of “Lokma” related with the history of eastern architecture. Lokma is the name of metal connectors used in railings, mostly inside of the openings of garden walls and old Mosque complexes. This system is often called “Lokma Railing” or “Lokma Iron”, while the connector of the railing is called […]


This is the second year we are experimenting a beautiful exercise with basic design 1 students at İstanbul Bilgi University Faculty of Architecture. This is the construction of new year’s lanterns to be lit at campus garden. Here are a few photos of the two projects from 2012 and 2013, taken by Avşar Gürpınar. As a geometrical basis for this, we are conducting unrolling and stellation exercises combined with the basic idea of platonic solids and archimedian solids in Rhino. Benay has also introduced some interesting examples of such constructions. Here […]


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 […]


Tetrahedron is a popular platonic solid for designers. We’ve explained how to draw them using equilateral triangles here before. Recently I’ve found (sorry, lost the web adress) a much quicker way of modeling a Tetrahedron using a cube. It’s very simple, just connecting the three opposite corners of the cube automatically makes them equal, resulting the four equal faces. Of course this time you’ll have to calculate the actual edge length, but if you use “box diagonal” command, you’ll also have opportunity to set the edge length of the tetrahedron. […]


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 […]


Octahedron is a platonic solid with 8 faces of identical equilateral triangles. It has a close relationship with cube as it’s dual. In order to construct an octahedron, we first have to create a square. Main problem of drawing the square is determining the right angle (perpendicular axis) to any point in euclidean space. We’ll draw it here as a two dimensional projection. However it can also be established in three dimensions with the same method (except using spheres instead of circles). Start from any two point in the space; […]


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 […]


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 […]


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. […]