I have some origami polyhedra which I know the type of faces it has and how they are connected (such as this torus) and I want to calculate the co-ordinates of the vertices to use as an input to script.
My question is how should I go about translating knowledge of the faces into the locations of the vertices? Are there geometric tricks I can apply? or are there any software libraries/tools I could use to help out here? To make thinks a bit more complicated I don't think all the faces are regular polygons, all the edges should be the same length and all the angles should be the same but being made of paper there is a little wiggle room.
A standard tool to do this sort of thing is the
polymakeprogram, which google will find in seconds.But from the description in your question (which is not very explicit) it seems that
polymakewould not work for you. For example, tori are not convex, and most things work on covex solds, and so on.