## dodecahedron

Becoming very popular after the Beijing 2008 Olympics National Aquatics Centre’s facade (which is believed to be a voronoi subdivision, as an epic mistake), Weaire-Phelan is a solution (again said to be the “best” solution, which is not yet proven) of equal volumes with minimal surface area. This quickly became a cult object for contemporary architectural geometry (this is correct). Although it is believed to be a structural solution, I think for architects, catching the eye with “cute bubbles” seem to be the primary purpose of this structure. (images from […]

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 […]