
Date: Mon, 16 Nov 1998 21:56:33 EST
Subject: Geometry
In analyzing a cube, I would like to find a tetrahedron inscribed in the cube which has none of its faces in the planes of the faces of the cube. I would like to see this tetrahedron outlined in the cube.
My name is Jane. I am an elementary education student.
Thank you!
Hi Jane,
The cube has eight vertices. Take four of them, which
do not share any edge of the cube (e.g. two opposite vertices
of the top square and two of the bottom  which are NOT
below the chosen top vertices).
Now consider these vertices as vertices of a tetrahedron.
You will find that the six edges you are looking for
are six diagonals of the six faces, joining the selected
vertices.
You will also find that you have 'chopped off' the other four vertices
with a plane through its three neighboring vertices, leaving
behind the four cuts as the four faces of the tetrahedron.


Walter
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