What does a reciprocal cone look like?

Question

I know the definition of a reciprocal cone, but still I am not able to visualise it. I couldn't find by searching on Google, can anyone please help?

Answer 1

As your question is about visualization, here is a graphical answer:

with orthogonal generating lines (as can be seen on the two thicker generating lines).

Connected: https://math.stackexchange.com/q/1714646.

Answer 2

made CW: see links below........

http://math.stackexchange.com/questions/1714136/condition-for-cones-to-be-reciprocal/1714646#1714646

http://math.stackexchange.com/questions/1899004/reciprocal-cone

http://math.stackexchange.com/questions/2077228/how-can-we-factorise-a-general-second-degree-expression/2077673#2077673

http://math.stackexchange.com/questions/2151112/show-that-the-cones-ayzbxzcxy-0-and-ax1-2by1-2cz1-2-0-are/2151866#2151866

Answer 3

Take any one generator of the cone. Draw a tangent plane to that generator. Tangent plane will pass through the vertex. Draw normal to this plane at the vertex. Repeat this for every generator of the cone. You will get a cone. This cone is called reciprocal cone.