Wolfram Demonstrations Project

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").

In 2D there are two right-angled triangles, corresponding to

and

; in 4D there are 24 simplices corresponding to

, etc.

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Simple Inequalities in the Unit Cube