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A triangular prism, which has 6 vertices and 5 faces.
3d shapes with six faces are called hexahedra.
cylinder
There are infinitely many shapes that do.
Hexagonal prism has percandicular faces
a triangular pyramid
cylinder
A cube has 6 faces
There are an infinite number of 3d shapes with more than 20 faces.
A tetrahedron (4 faces) and an icosahedron (20).
Polyhedra (singular = polyhedron).
Spheres