This is the Grasshopper definition that generates tetrahedral helix (also called as Boerdijk-Coxeter helix), but in a funny way. This geometry is also a solution for tangent spheres. I generated the helix using Anemone components for recursion and gave it a little bit of responsiveness. I don’t know if it depends on the speed of your CPU but if it is slow enough, you’ll see the snake game of tetrahedral helix as it is driven by your input from a control knob. I’m not that interested in phone apps nowadays but […]

## tetrahedron

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. […]

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 […]

Truncated Tetrahedron is an Archimedian Solid, created by slicing a Tetrahedron. It’s faces are regular hexagons and triangles. Assuming you’ve created a Tetrahedron, first join it’s faces to create a polysurface. Now, you may re-create the lines of 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 By/Number of Segments) and type 3 to the number of segments to be created. Now all edges should be divided equally into three parts. Draw the equilateral triangles, connecting the […]

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. […]