"Unfolding" A body in 3D

Mylenium suggesting exploring with Trapcode Mir or Plexus would be much more intuitive to get some interesting faceted designs. Your approach to this should also be dictated by how long this effect should last. If it is a quick transition, I would suggest creating a simple matte with triangles fading in or out as you suggested as a kind of cheat. If you want a more intentional and drawn-out effect then perhaps a variation of your approach could work.

The important thing is to ensure each triangle you make begins as a triangle with a solid flat base. Meaning - You'll need a flat edge for your anchor point to sit on, that way you can unfold it properly. 

If you want to have layers unfolding how you describe, I would start with an entirely unfolded design in AI or PS and map out how each triangle should fold. This way you have a plan to reference in AE and know which edge each triangle will unfold from.

Then isolate each triangle as its own layer and reorient them so that the edge of each triangle shares the same axis (reference my image attached.) This way you can re-layout all your individual triangles in AE using your original reference. It is important that each triangles anchor point is set to the edge that needs to unfold. Once you have each triangle laid out in it's unfolded resting position as a 3d layer, you can focus on folding them working backward. Each triangle can fold on its proper axis and can be trimmed when you need it to.

This is a manual effect that requires you to build a rig to control the folding and allow you to make tweaks to animation afterward. There is definitely more to talk about to get a quality effect but this may be a direction you can explore.

Mylenium suggesting exploring with Trapcode Mir or Plexus would be much more intuitive to get some interesting faceted designs. Your approach to this should also be dictated by how long this effect should last. If it is a quick transition, I would suggest creating a simple matte with triangles fading in or out as you suggested as a kind of cheat. If you want a more intentional and drawn-out effect then perhaps a variation of your approach could work.

The important thing is to ensure each triangle you make begins as a triangle with a solid flat base. Meaning - You'll need a flat edge for your anchor point to sit on, that way you can unfold it properly. 

If you want to have layers unfolding how you describe, I would start with an entirely unfolded design in AI or PS and map out how each triangle should fold. This way you have a plan to reference in AE and know which edge each triangle will unfold from.

Then isolate each triangle as its own layer and reorient them so that the edge of each triangle shares the same axis (reference my image attached.) This way you can re-layout all your individual triangles in AE using your original reference. It is important that each triangles anchor point is set to the edge that needs to unfold. Once you have each triangle laid out in it's unfolded resting position as a 3d layer, you can focus on folding them working backward. Each triangle can fold on its proper axis and can be trimmed when you need it to.

This is a manual effect that requires you to build a rig to control the folding and allow you to make tweaks to animation afterward. There is definitely more to talk about to get a quality effect but this may be a direction you can explore.

No easy solutions. This will always be "clunky" on some level and would be anything but trivial even in a 3D program or with the help of plug-ins in AE. It's easy enough to get a bunch of random triangles to appear somewhere, but a controlled, organic unfolding spread, adapted to existing motion is a whole different thing. As far as that goes, you might want to have a look at tools like Plexus or Trapcode MIR, but even then it's going to require lots of manual labor to push around Nulls and other auxiliary layers in 3D space in addition to the actual masking.

Mylenium