An octahedron is a closed 3-d shape with 8 polygonal faces. There are 257 topologically different convex octahedra. One of the 257 is a quadrilateral based dipyramid. A special case of this shape a square based right dipyramid. So a special case of one out of 257 possible convex versions is regular. However, despite the fact that the vast majority of octahedra are not regular, the term is often used to refer to the regular version.
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Many options. A pentagonal prism or a regular octahedron, for example.
A regular tetrahedron. octahedron, dodecahedron.
Start with an octahedron in the form of a quadrilateral based dipyramid a regular octahedron is a special case of this). This shape has six vertices - chop these off so as to remove a quadrilateral based pyramid. You will be left with a truncated octahedron. It is an octahedron which has been truncated (shortened) by cutting off its extremities.
An octahedron is not a polygon. A polygon is a two dimensional shape. An octahedron is a three dimensional shape and is classified as a polyhedron.
There are 257 topologically different convex octahedra. A special case of one of these is regular: other cases of that shape and all other octahedra are not regular.