2x2x2x2 hypercubes and binary quartic forms

In 2001, Manjul Bhargava proved a composition law for 2x2x2 cubes which generalized Gauss composition of binary quadratic forms by showing that a triple of binary quadratic forms arising from a cube sum to zero in the class group. This is referred to as the Cube law.
In a subsequent work, Bhargava and his student Wei Ho studied the space of 2x2x2x2 hypercubes and proved orbit parametrizations of this space by certain data involving genus one curves. The parametrization relies on a quadruple of binary quartic forms that arise from a hypercube via a slicing technique. In this talk, we will explore the relationship between the hypercubes and binary quartic forms and present an analog of cube law for the binary quartic forms arising from a hypercube