# Regular hexagon in a cube

Given a block of cheese in the shape of a cube.
Give a symmetry argument for why it is possible to make a single cut
through the block of cheese such that the two cut faces are regular hexagons.
Is there a way to make a single cut so that the two cut faces are equilateral triangles?
If yes, how? If no, why not?
Is there a way to make a single cut so that the two cut faces are squares?
If yes, how? If no, why not?

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