Ment
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Okay, let's consider this:
Imagine we are constructing polyhedra and implementing them, endowing them with weight. Obviously, we can construct a polyhedron such that, when placed on a flat horizontal plane (on one of its faces, or even on all its faces in turn), it remains in a state of rest, in equilibrium. At the same time, such a polyhedron can be irregular.
Question: is it possible to create such a polyhedron so that it would not be in a state of equilibrium (it would tip over) when placed on any of its faces? In other words, would there be no face from which it would not tip over?
Of course, this can be proven.
Imagine we are constructing polyhedra and implementing them, endowing them with weight. Obviously, we can construct a polyhedron such that, when placed on a flat horizontal plane (on one of its faces, or even on all its faces in turn), it remains in a state of rest, in equilibrium. At the same time, such a polyhedron can be irregular.
Question: is it possible to create such a polyhedron so that it would not be in a state of equilibrium (it would tip over) when placed on any of its faces? In other words, would there be no face from which it would not tip over?
Of course, this can be proven.