Finite self-similarity conjecture for finite simplicial complexes

A finite simplicial complex is the topological space obtained by gluing finitely many simplices along faces. A compact metrizable space is finitely self-similar if it arises from a finite self-similarity system, meaning that its self-similarity equations involve only finitely many spaces. Finite self-simplicial-complex conjecture. Every finite simplicial complex is finitely self-similar.

The standard simplices are finitely self-similar, and the conjecture asserts that this property is preserved when finitely many simplices are glued along faces; for example, gluing two intervals produces a circle. The source presents this as a conjecture and gives no resolution.