  The Vicsek model of self-propelled particles is known in three different
phases: (i) a polar ordered homogeneous phase also called Toner-Tu phase, (iii)
a phase of polar ordered regularly arranged high density bands (waves) with
surrounding low density regions without polar order and (iv) a homogeneous
phase without polar order. It has been questioned whether the band phase (iii)
should be divided into two parts [Chat\'e2020]: one with periodically arranged
and one with strongly interacting but not ordered bands. We answer this
question by showing that the standard Vicsek model has a fourth phase for large
system sizes: (ii) a polar ordered cross sea phase. Close to the transition
towards (i) this phase becomes unstable and looks like strongly interacting
bands. We demonstrate that the cross sea phase is not just a superposition of
two waves, but it is an independent complex pattern. Furthermore we show that
there is a non-zero mass flow through the structure of the cross sea pattern
within its co-moving frame.
