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What is the minimum number of TET elements you need, in order to fully fill a cube(HEX element)?

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    $\begingroup$ Do you have any additional criteria besides fewest elements? If I'm understanding correctly, the answer would be 2, as you can create two tetrahedral elements by splitting a cube in half through two opposite vertices. But that won't necessarily yield good results. $\endgroup$ May 27, 2015 at 15:31
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    $\begingroup$ @Trevor: It doesn't work that way. There is no cutting plane you can appply to a cube to end up with two tetrahedrons. $\endgroup$ May 27, 2015 at 19:40
  • $\begingroup$ @OlinLathrop Yep, you're right. Took me a while to figure out what I was missing since I didn't have a cube in front of me. $\endgroup$ May 29, 2015 at 11:54

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5 tet elements

Image 1: 5 tetrahedral elements can form a cube.

This video shows how to decompose a cube into five tetrahedra. Not saying it can't be done with less, but I can't figure out how :-)

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    $\begingroup$ "Not saying it can't be done with less:" It's easy to show you need at least 5 tets. A cube has 8 vertices (corners). One tet has 4 vertices. If you build a mesh by adding an element which shares a face with the previously assembled elements, you add at most one more vertex. (In some situations, adding the element might not add any new vertices.) So to get 8 vertices, you need at least 5 elements. And the picture shows you can indeed do it with at most 5 elements. $\endgroup$
    – alephzero
    Jun 13, 2015 at 21:18

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