This article provides a direct calculation of the 4-particle amplituhedron at
3-loop order, by introducing a set of practical tricks. After delicately
rearranging each piece of this calculation, we find a suggestive connection
between positivity conditions and Mondrian diagrams, which will be
quantitatively defined. Such a pattern can be generalized for all Mondrian
diagrams among all those contribute to the 4-particle integrand of planar N=4
SYM to all loop orders, as a subsequent work 1712.09994 will show.Comment: 32 pages, 3 figures, 1 appendix. Figures improved for v
