Some hexahedra are prisms or pyramids.
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Yes if it has a unified hexagonal cross-section
A hexahedron is a 3D shape with 6 faces. It CAN be a prism whose base is a square. But that is only one example. It can also be a prism whose base is any quadrilateral. It can also be something like a pentagonal pyramid (i.e. the base is a pentagon and the sides are made up of 5 triangles.)
The generic term is a hexahedron. It can be a pentagonal pyramid, or a quadrilateral prism (or a more irregular version of that).
No, it is not.
A pentagonal pyramid is a hexahedron with a pentagonal face.