#polyhedra

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 them is very suitable to implement on Grasshopper’s VB component….

An octahedron is a polyhedron and platonic solid with 8 faces of identical equilateral triangles. In this post, I will try to explain the drawing and unrolling process of the octahedron. It has a close relationship with the cube as it’s dual. In order to construct an octahedron, we first have to create a square. The 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…

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 and c, with a radius of a to c. The…

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 Icosahedron below; First, you should create an Icosahedron, the Platonic…

Today’s polyhedra is the beautiful icosahedron. It is one of the five Platonic Solids with twenty equilateral triangular faces. Its dual is the dodecahedron, which has pentagonal faces. Here, I explained the process of modeling an icosahedron. 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 with a radius of the pentagon’s edges. You can exercise Tetrahedron to understand how we find a point…

A truncated tetrahedron is an Archimedean solid, created by slicing a tetrahedron. Its faces are regular hexagons and triangles. Assuming you’ve created a tetrahedron, first join its faces to create a closed polysurface. Now, you may recreate the lines of the tetrahedron’s edges, either by drawing them or generating them (Curve / Curve from Objects / Duplicate Edge). While the edge lines are selected, hit (Curve / Point Object / Divide Curve / Number of Segments) and type 3 to create…

The tetrahedron is a platonic solid with four equal triangular faces (equilateral), six equal edges, and four vertices. In the construction of a tetrahedron, we will look closer at length transfers using compass-like tools in two- and three-dimensional space. To define the edge length of the first triangle, start with any two points in Cartesian space. Using a compass (arc or circle), draw two arches (or circles) using your initial points as corners and the distance between your points as…