There cannot be a 3-d shape all of whose faces are regular hexagons.
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that claim above is not true, because for example a classic soccerball consists of hexagons.
It's called, not altogether surprisingly, a hexagonal prism. If the bases were hexagons and the other faces were triangles, it would be a hexagonal antiprism.
If by faces you mean sides, then lots. Parallelograms and squares come to mind but I'm sure there are more (hexagons for would be another).
A hexahedron is a three-dimensional figure with six identical faces - in other words, a cube. So a hexahedron is not made up of hexagons at all, but of squares. However, if you were to balance a cube on one of the vertices, the horizontal plane cutting the cube in half would make a cut in the shape of a regular hexagon. Four such regular hexagons can be found in the cube.
I would mostly say yes if it was a cube but I don't know
If by "vertex," you mean "apex," than any pyramid would fit the description.
The 3d shape that have five faces would be a triangular prism **************** or a pyramid
Since a cube has 6 faces, you would be looking for a solid shape with only 2 faces and no such solid exists.
the other faces on a pentagonal prism would be rectangular
Its a Octagon * * * * * No. An octagon is a shape with 8 sides. 8 faces implies a 3-dimensional object, which would have to be an octahedron.
A cuboid would fit the given description which has 6 faces, 12 edges and 8 vertices
The shape would be impossible. The faces and vertices have to add up to two more than the edges.
Assuming the shape is a simply connected polyhedron, there are 6 faces. A triangular dipyramid, for example.