What is the position of the dual of a plane in 3D space [closed]

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I have a cube and a plane q that intersects the cube at one of its vertex v. Under dual transformation in geometry, the dual of a point in 3D is a plane and vice versa. The dual of a cube is an octahedron, where a vertex of the cube now becomes a face of the octehedron, and a face of the cube becomes a vertex of the octehedron.

Now what I want to know is where the dual of the plane q is. As q intersects the cube at vertex v, does it lie on the face (that corresponds to the dual of v) of the octahedron? Anyone can help me out on this problem? Thanks a lot!

Answer 1

Yes, sure. In the primal, the plane q is incident to the vertex v. Thus in the dual, dual(v) and dual(q) are also incident. That means that the dual(q) is a vertex that lies on the face dual(v).