He talks all about how the Amplitudihedron computes the same result for the scattering amplitudes as ordinary peturbation theory in a simple and elegant way, but I fail to understand how one actually computes the Amplitudihedron for a certain scattering process anyway?
As per the recent TRF posts about Amplitudihedrons and why they don't wear diapers, I can understand that one may calculate the scattering amplitudes by simply taking the volume of the Amplitudihedrons (ignoring constants, I guess), but how does one actually calculate the amplituhedron?
I'm especially stunned by the image (looks like a sort of a concrete example, don't know how they constructed the amplituhedron):
To summarise my question, how does one actually figure out, or construct, the amplituhedron based on the specific scattzering process?
Wait for the paper. It's a geometric object in some space whose dimension depends on the number of external particles, number of loops, and number of "helicity flips". The volume form, the integrand, is a simple form roughly scaling like $ 1/x $ where $ x $ is the distance from a face, and the faces are given by inequalities of the type "determinants of a submatrix are zero". These inequalities depend on the external momenta and/or twistor variables, sort of linearly or simply. The scattering amplitude is the single simple integral of the volume form over the polytope.