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A polyhedron is a generic term to describe a closed 3-dimensional (solid) shape that is bounded by polygons. It can have 4 or more faces - any number.
3d shapes with plane faces are called polyhedra (singular = polyhedron). The minimum number of vertices is 4, there is no maximum.
Tetrahedron
Yes: the tetrahedron.
A regular polyhedron has equal size faces as in the case of a tetrahedron which is a triangular base pyramid that has 4 equilateral triangle faces.