Did you know that the diagonals of the faces of a cube can be joined to form the framework of a tetrahedron?

Asked by LostInParadise (32183

) October 4th, 2016

I just read about this today. It seems that things should not work out so nicely. It would be nice to see a sculpture of the cube with a tetrahedron inside it.

Choose a face of a cube and draw a diagonal on it. The vertices at each end of the diagonal are shared by two other faces. From each vertex draw the connecting diagonals to the two other faces. That leaves one more face to be connected to the others. The lines form the outline of a tetrahedron.

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2 Answers

I just drew it. Amasing!

Sneki95 (7017

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I found a picture

Some other interesting facts:
The tetrahedron uses half the cube’s 8 vertices and one of the two diagonals on each face. The other 4 vertices can be linked together to form the same type of tetrahedron using the other diagonals.

The volume of the tetrahedron is ⅓ the volume of the cube, which is the same volume you would get from a square pyramid whose base was on one of the faces and which has the same height as the cube.

LostInParadise (32183

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