How to create equal triangle or polygon surface on a statue? (irregular surface)

My goal is to create a 3d print a dog mesh frame with equal triangles or polygons.
(Please refer to image)

Whole idea is to laser cut acrylic into equal triangle and insert them into dog mesh frame.

Therefore, I should have least amount of different shapes, which is different size of equal triangles.

What are some apps/plugins out there that can help achieve my goal?

Thanks ahead.