Wiktionary
bicone
n. (context geometry English) The three-dimensional shape swept by revolving an isosceles triangle around its edge of unequal length, or by joining two identical right circular cones base-to-base.
Wikipedia
Bicone
A bicone or dicone (''bi- comes from Latin, di-'' from Greek) is the three-dimensional surface of revolution of a rhombus around one of its axes of symmetry. Equivalently, a bicone is the surface created by joining two congruent right circular cones base-to-base.
A bicone has circular symmetry and orthogonal bilateral symmetry.