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Select all the tirangles and make them a Compound Path (Object > Compound Path > Make).
Add the image to the selection, and choose Object > Clipping Mask > Make.
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in addition to John's message: make sure that there are gaps between the triangles, otherwise, they will look like a solid shape.
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If I understand correctly:
Make a copy of the triangles.
Select all the triangles and unite them in the pathfinder.
Use the result as clipping mask.
Paste the copy in front, fill with none and give it a stroke.