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There are many such shapes: a sphere, ellipsoid, toroid all have no flat faces.

Any one of the intersected by one plane will have one flat face, if intersected by two planes, there will be two and so on.

Amongst polyhedra, only a tetrahedron (or triangular prism) fas fewer than 5 flat faces.

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Q: Which solid have fewer than 5 flat faces?
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