3d shapes with six faces are called hexahedra.
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hexagon.
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pentagonal pyramid
A hexahedron. An example is the cube; the cube has six equal faces and is three-dimensional.
For a 6 sided shape to be a hexagon, it must (in addition to having 6 sides) be a polygon. To be a polygon, it must be a closed shape (no unlinked lines) and it must be convex (All angles are pointed towards the outside, rather than inwards). If it matches all of these criteria, then it is indeed a hexagon. There are many 6 sided shapes that are not hexagons, including cubes.