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A binode is a double point of a surface whose tangent cone consists of two different planes.
A plane is found in two dimensions; a surface is part of a three-dimension object, including possibly a set of planes, such as a cube or a pyramid.
The angle between two planes when the planes intersect at a point is the acute angle fixed by the normal vectors of the planes.
Between 2 distinct points, there are an infinite number of planes that can be drawn in 3 dimensions
A Dogfight.