modular paneling problems

hi everyone,

i'm very VERY new at this, so i apologise if this is a silly question:
i'm trying to apply panelling to a surface (from the research i've done, this seems do-able), but i need the panels to be triangular (not square, and not a diagrid) and modular (+ therefore not warped by the projection onto the surface).

hard to explain. i've attached the file of the module. (the surface i want to panel isn't important, i just need it to be editable.)

each of the triangles needs to be dependent on the ones around it, so that the modules can change shape, (fold and turn inside out) but also needs to stay the same size (this needs to be built out of all one sized panel) which is why i've made surfaces between the points of the line. but really, i dont know if this is the right way to go about it at all.

if anyone has any tips on how i could go about this (or if it is even possible) it would be greatly appreciated.

thanks,
mhairi.