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.
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A regular octahedron is one of the platonic solids. Each of its faces is an equilateral triangle.
A regular octahedron.
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.
Many options. A pentagonal prism or a regular octahedron, for example.
A tetrahedron, cube, octahedron, dodecahdron and icosahedron.