10 · Regular lifting
Lift, support, project.
Cube points receive height zero and added points height one. The equality set of ℓS cuts out one lower facet—and therefore one prism cell.
cube point, height 0 added point, height 1 equality set
Each vertical segment is one exact slack.
This is a comparison chart, not a picture of four-dimensional space. A zero-length segment means ω(v) = ℓS(v), so that defining point belongs to the lower face projecting to PS.
Project the equality faceThe selected lower face lands on P{2,3} in the G₃ subdivision.