We study the number of extremal elements of smooth cones in the first orthant under bisection. We give a criterion for a smooth cone to be an extremal element under bisection, and prove that the number is equal to the number of equivalent classes of integer points in the region of a real algebraic variety cut by hyperplanes. In 2 dimensional case, we prove the uniqueness of extremal element. In 3 dimensional and higher cases, we can only prove that there are infinite extremal elements.
