If all the faces are triangular and all the edges are of equal length the only thing left to vary is the number of triangles meeting at each vertex.
Try looking up deltahedra
Also, if the surface need not be closed you can get some interesting effects by joining >6 triangles around a vertex. See Edmund Harriss's post here
You won't be able to make a smoothly curved surface with only equilateral triangles.
The curvature of a mesh comes from the deficit or excess angle at each vertex (giving +ve and -ve Gaussian curvature respectively). For the mesh to appear smooth these angles need to be small, but if you limit yourself to equilateral triangles they can only be multiples of pi/3.
I suppose you could make a rather blocky/spiky approximation of an arbitrary surface with equilateral triangles, just as you can approximate an arbitrary surface with cubes.
I'm also very interested in finding a technique to do this.... at the moment I don't care so much about replicating the base surface exactly, I want to use the NURBS surface as a kind of idealized control, and generate a triangulated surface that's composed of identical pieces. for my purposes the triangles don't have to be equilateral, but I would like them to be identical, or limited to a set of n different types.
is there a way (in GH or in Rhino, or with some other plugin) to do this? I'm trying to think about construction costs of the panel system while I build up my base geometry, so it would be incredibly useful to constrain the geometry to a handful of different panel types.
It seems like the Mesh components in GH are fairly powerful (and complex)... could you explain how one would go about limiting the mesh to certain angles and certain edge lengths?
There is a command to produce equal divisions from a surface called ptGridSurfaceDistance.
With the new version you can plug the panelling tool to Grasshopper (check out the manual).
Currently i'm doing my thesis on structures composed of equilateral triangles. There is a french architect, Alain Lobel, who wrote some code in C# to generate grids which are solely composed of equilateral triangles. His website is www.equilatere.net I already tried to contact the man, but i had no response. :( Maybe you have more luck than me.
Wow his work is brilliant!
I'll try my luck (i'm also french it might help :)) it d be great if we could do something like that on GH. I think the forms were generated from the equilateral triangle as opposed to applying an equilateral pattern onto a form...It's a very different process isn't it?
I feel this could fit into Giulio's Weaverbird...
Arthur
You are right. In order to generate his structures he started from the equilateral triangle. He wanted to know which forms are possible by using solely the equilateral triangle. It is an other approach but sometimes an other point of view can give inspiration. :)
As a matter of fact, I'm focusing on these Lobel frames in my thesis. In a topic I launched recently (http://www.grasshopper3d.com/forum/topics/simulation-of-a-deployable) you will find a manner to generate one of his structures by using GH. I know it's not a rock solid solution but maybe it can inspire you.
I have no experience at all with weaverbird.
I don't know if it's allowed to refer to other discussions. If not, sorry. It's not my intention to highjack your discussion. ;)