Higher-order interactions · simplicial models
A project team can discuss scope with the scheduler, and scope with the resource manager, without ever settling a joint scope–schedule–resources decision. These four toy examples distinguish pairwise links from a declared three-way relationship.
Filled face: a three-way relationship is included in this toy model. Outline: its three pairwise links are included, but that three-way relationship is not.
Choose a case to highlight its triangle. All cases remain listed for keyboard and screen-reader access.
A vertex names a concern. An edge records a pairwise relationship. A 2-simplex is a filled triangle together with its three edges and vertices: it records one additional joint relationship. Its boundary alone is a three-edge cycle, not a 2-simplex.
The drawing is a projection of an abstract simplicial complex. Crossing lines do not introduce extra vertices, and visual overlap does not create extra faces. A triangle left unfilled is not, by itself, a calculation of a topological hole.
Pick three concerns in your project. Name the joint decision, commitment or constraint that would justify adding a filled face. Who can check that decision across all three? What evidence would change your model?
These relationships are illustrative choices. A filled face does not establish agreement, beneficial coupling or feasibility; an outline does not predict failure. This app runs no cost, schedule, risk simulation or topological analysis.