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Simple Inequalities in the Unit Cube

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Permute the triple , , in all six possible ways and form the six corresponding inequalities , , etc. Plot these relations in 3D with to split the unit cube into six congruent right-angled tetrahedra (called "orthoschemes").

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In 2D there are two right-angled triangles, corresponding to and ; in 4D there are 24 simplices corresponding to , etc.

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Contributed by: George Beck (September 2007)
Open content licensed under CC BY-NC-SA

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