  We elaborate the two-fold simplex-like structures of tree amplitudes in
planar maximally supersymmetric Yang-Mills (N=4 SYM), through its connection to
a mathematical structure known as the positive Grassmannian. Exploiting the
reduced Grassmannian geometry and the matrix form of on-shell recursion
relation in terms of super momentum twistors, we manifest that tree amplitudes
can be remarkably refined via the essential building blocks named as
fully-spanning cells. For a fixed number of negative helicities, an amplitude
can be entirely captured by finite, compact information of the relevant
fully-spanning cells up to an arbitrarily large number of external particles.
