There are some paradoxes in the composition relationship between point-line-plane-space. I found that a numerical example of Russell's paradox- ∅Pan -can solve these problems. ∅Pan is a set group that all its sets are mutually included. Geometric ∅Pan has remarkable properties that all its lines are mutually included and mutually iterated, and the same as planes and spaces. Visualization models for these geometric set groups were established through cross-composing timelines, cross-monitoring screens, and cross-sharing cyberspaces, respectively. These findings demonstrate that sets/objects can mutually include and geometries/objects can mutually iterate. I anticipate the present paper to be a starting point for a novel kind of set group and algebraic geometry.