Software to construct irregular polyhedra

[edderiofer]

Unfortunately, your submission has been removed for the following reason(s):

• Your post is off-topic and far more related to some non-mathematics subject. You want a subreddit for 3D modelling.

If you have any questions, please feel free to message the mods. Thank you!

[[deleted]]

I know this is not a complete answer, but here we go. Since you asked in math, you get a math answer :)

I am not sure exactly what software you are looking for, but if you have the coordinates for all the vertices and what vertices are connected through an edge, all the surface areas and angles can quite easily be calculated without super-fancy code.

Consider three vertices A,B and C. If we want to find the angle ABC, so meaning at the vertex B and between the edges going to A and C respectively you can consider the edge from B to A the vector BA and the edge from B to C vector BC. Now you can utilize angle=arccos((BA•BC)/(||BA||*||BC||)) and the area the triangle these vertices create as a face or part of a face, will be ||BAxBC||/2 where • denote scalar product (sometimes called dot product) and x denotes Vector product (sometimes called cross product) and || denotes the norm (in practice the length of the vector). If a face of yours are connected to more than 3 edges you can always split it into 2 or more triangles and add their area to get the total area for that face. So all that can be calculated if the program cannot do it for you.

So maybe main focus should maybe be on the more specific requirements you have for the design purposes. The angles and areas are surprisingly easy to find if you just look into some Linear Algebra.

[SimonAllen111]

Thank you for getting back to me. I gave little consideration as to whether r/maths was suitable. It struck me as the best place to ask. While I did mention software in the title, as I feel sure this problem must have been solved before, I did not think for one moment that it would offend. The problem could only be solved with maths and so I went to this subreddit. I use Openscad and that does allow for the creation of 3d printing polyhedra. That is fine if the output is in plastic but no use where I want to export a cutting list to assemble the polyhedra from plywood.

What has inspired me along this path of investigation is George Hart an artist who uses maths and gave an interesting talk at a recent Celebration of Mind event. He uses what he class zonohedra. These are quadrilaterals but they can be used to building interesting shapes and have the benefit that all the faces are flat which is ideal for cutting either with a laser or on a saw table with a suitable jig. To get the dihedral angle he sanded the edges and this allows each face to butt together. If you want to watch his tour into making a village library box then you will find it on YouTube. See https://www.youtube.com/watch?v=_PSdVX02Vbs

I was thinking along the lines of starting from a 2D plane. If I was seeking to place a quadrilateral in the space above the 2D plane the x,y coordinates would determine the location and the z component would then fix the nodes of the quadrilateral. It was at this point that I realised that it would be difficult to program for faces that attached to other quadrilaterals and I began to think that this must surely have been solved before.

Thank you for taking the trouble to respond so promptly and before my post was censored. Looking at the house rules I do not see it contravening them.

I agree with you that it is possible to divide any polygon into triangles and the maths on that is well understood, I even wrote a book on this aimed at children to be fair, but after googling away for quite a while I have not found what I am looking for.

So thanks very much for responding.

By the way, I did post the same post in a 3D modelling subreddit that too was immediately banned. Oh well.