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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).

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  • $\begingroup$ Thank you so much, if I can just know now how to create the original triangular pyramid. Let me know what I can do in return even if you don't know how to do this! $\endgroup$
    – user1802
    Dec 9, 2013 at 12:15
  • $\begingroup$ @user1802 Do you mean a regular tetrahedron? There are several ways to make such shape. Typically, you may enable an addon called Regular Solids, which can make one much easier. $\endgroup$ Dec 9, 2013 at 12:29
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    $\begingroup$ You can add a Mesh Circle and set Vertices to 3, fill type to Triangle Fan. Move the center vert up, deselect, select the 3 bottom verts and make face for your triangular pyramid. Then poke faces. $\endgroup$
    – CodeManX
    Dec 9, 2013 at 16:49

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