bicones

A bicone is a geometric solid formed by two congruent right circular cones that share a common base. The apexes of the cones lie on opposite sides of the base, resulting in a symmetrical figure with an axis of rotational symmetry. Most often, the term refers to two identical cones base-to-base, though a non-congruent double-cone shape is sometimes described in similar terms.

If each cone has base radius r and height h, the overall height of the bicone is 2h. The volume is the sum of the volumes of the two cones, giving V = (2/3) π r^2 h. The external surface area consists of the two lateral conical surfaces only, since the shared base is internal; this area is A = 2 π r l, where l is the slant height with l = sqrt(r^2 + h^2). The base circle is not exposed in this solid. The centroid of a symmetric bicone made of identical cones lies in the base plane, halfway between the two apexes.

In practical contexts, bicones appear in two notable forms. In mathematics and education, they serve as a simple example of a double-cone solid. In jewelry and decorative arts, a bicone is a common bead or crystal shape cut into two cone-like halves, often with a hole along the axis for stringing. Crystal manufacturers frequently refer to two-cone cuts as bicones, valued for their sharp points and reflective facets.

Overall, the bicone is a straightforward yet useful model of two cones joined base-to-base, with clear geometric properties and several real-world applications.