paneling a sphere without dupicates + contructional dilema

Hello guys. 

The goal of the attached definition is to produce a "lamp", where the pipe construction will be 3D printed and the triangles (that come from the paneling component) will be CNC milled.

Due to constrains, I HAVE to do it like this (I can't 3D print everything or opposite).

First 

I have no idea how to make the panels, without so many duplicate Edges, Faces etc.

Second 

I can't figure out how to align the triangle panels to fit in the construction, so it can be assembled ideally without glue. This problem is both conceptual (I can't figure out how to do it fiscally) and grasshoper-wise - I don't know how to organize data list and produce a global movement, so that the triangle parts do not intersect with each other, BUT intersect the 3d printed construction part (where they fit fix in or just fit and can be glued).

Triangles will be milled out from 3mm Plexiglas, BUT I will not have an option to mill at an angle, so only 90° edges.

3D printed parts will be executed by a high level production powder printer, so it should hold good.

Any ideas?

best,

cuki