How could I make triangular pyramids on each face of an original triangular pyramid.
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If I didn't misunderstand your question, you can switch to Edit Mode, Make sure all faces are selected by pressing A, then AltP to poke faces, which will create a vertex on each face. Tweak Poke Offset value in its setting panel down to the left-hand Tool Shelf.(or press F6 to call a separate popup).