dodecahedron

I had been researching Goldberg Polyhedra for a while. While exploring how to perform chamfer operations in Grasshopper, I found some interesting results. I want to share them with you. In this Grasshopper project, I reused my previous work, where I built a dodecahedron using…

In geometry, the excavated dodecahedron is a star polyhedron that looks like a dodecahedron with concave pentagonal pyramids in place of its faces. In this short tutorial video, I am modeling an excavated dodecahedron in the Rhinoceros software. I use basic drawing and modeling commands….

A dodecahedron is a three-dimensional polyhedron with twelve flat, regular pentagonal faces, twenty vertices, and thirty edges. It is one of the Platonic solids and is highly symmetrical, with each face being a regular pentagon. The dodecahedron’s shape is unique among the Platonic solids because…

Modeling a rhombicosidodecahedron requires exploding and extending the faces of a dodecahedron and an icosahedron of the same edge length. We begin with both polyhedra centered at the same point. Then, we explode the faces of the dodecahedron and icosahedron outward from the center. We…

An Archimedean solid is a convex isogonal (vertex-transitive) and nonprismatic solid that is composed of two or more regular polygonal faces. There are thirteen such solids in geometry. Coding the snub dodecahedron study aims to generate one of these solids, composed of 12 regular pentagons,…

Here is a method for coding the dodecahedron and all its irregular variants in Grasshopper as quickly as possible. I utilized the golden ratio rectangles, usually used to construct the sister polyhedron, the icosahedron. However, the magic component of the Grasshopper, the Faceted Dome rescued…

The regular dodecahedron is one of the five Platonic solids, characterized by having 12 regular pentagonal faces, 20 vertices, and 30 edges. When you elongate it, you extend its structure in one or more directions, resulting in a shape that retains the basic properties of…

This is a 3d modeling tutorial for the platonic solid of dodecahedron. Modeling a dodecahedron is a good exercise for the basic transformation commands such as Rotate3D in Rhinoceros. You will see that it is possible to calculate the rotation angle by using sphere intersections….

The rhombic dodecahedron is a polyhedron with twelve rhombus-shaped faces, where each face has four sides of equal length. It is possible to construct the space-filling variant of the rhombic dodecahedron by arranging multiple such rhombic dodecahedra in a regular pattern so that they fill…

The Weaire-Phelan structure is an optimal solution to the problem of partitioning space into equal volumes with the least surface area. Denis Weaire and Robert Phelan discovered it in 1993. This structure gained attention due to its efficiency in filling space, offering a configuration that…

Becoming popular after the Beijing 2008 Olympics National Aquatics Centre‘s facade (which is believed to be a Voronoi subdivision, as an epic mistake), the Weaire Phelan structure is a solution of equal volumes with minimal surface area. This nice website briefly explains the phenomenon. There…

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,…

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…