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Is there a name for a 3d convex shape made of 8 arbitrary points ?
That would be like a cube or a box, except that the distances would not necessarily be equals, neither the angles necessarily be right angles.
In 2D, the equivalent would be a convex quadrilateral, but how do we translate this concept in 3D ?

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I don't think there's a name, apart from polytope (the equivalent 2-D terms is polygon). There isn't anything too special about 4 random points in the plane, as opposed to 5, 6, 7, ... – Calvin Lin Jan 16 '13 at 11:19
A convex polytope with 8 vertices will generally have triangular faces, not quadrilateral faces, so it will be quite different from a box. I don't think it has a name, although a 3-D polytope with 4 vertices is called a 3-simplex. – Hew Wolff Jan 16 '13 at 20:57
@CalvinLin and HewWolff Thank you for mentioning the "polytope" term, so it seems the closest to my "deformed box". – wil Jan 17 '13 at 2:11
A polytope in 3D is called a polyhedron, just like a polytope in 2D is a polygon. If your polyhedron is so much like a box that it has six quadrilateral faces, it would be a hexahedron. – Rahul Jul 12 '15 at 20:11
It sounds like you may also be interested in the "convex hull" of 8 points. – Mark S. Apr 9 at 16:14

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