Looks like that graphic was probably created in a 3D app. Naturally, you could make something like that by drawing a bunch of triangles, and position all of the points with View / Snap to Point enabled.
As far as coloring it, you'd just have to do it piece by piece.
There are a number approaches you could take.
One might be to simply set color and transparency for each piece.
Another might take this a step further by duplicating the finished triangle components and Pathfinder / Unite. Then place the united component in a layer below the main component. Then you could fill the united component with an interesting gradient or something. Then for the main triangles you could experiment with different transparency modes.