¶ Tetrahedron: Coordinate Symmetry
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Index Entry
Tetrahedron: Coordinate Symmetry:
“I am going to have a cheese tetrahedron and I am going to slice parallel to one of its faces, and what is left is still a regular tetrahedron and all the edges are equal. I can now slice parallel to one of its other four faces, and it is a smaller tetrahedron but it is still regular and symmetrical. I slice parallel to the third face and it is smaller still but still symmetrical. I slice parallel to the fourth face and what remains is still symmetrical. Then we take any other symmetrical geometry, such as a cube, and I am going to slice parallel to one of its faces, and what is left over is no longer symmetrical. I try it with an octahedron and slice parallel to one of its faces, and what is left over is not symmetrical. In fact, if you try all the other symmetrical geometries, only the tetrahedron has an integrity of symmetry independent of local alterations…”
