When individuals interact with each other and meaningfully contribute toward a common goal, it results in a collaboration. The artifacts resulting from collaborations are best captured using a hypergraph model, whereas the relation of who has collaborated with whom is best captured via an abstract simplicial complex (SC). We propose a generative algorithm GENESCs for SCs modeling fundamental collaboration relations. The proposed network growth process favors attachment that is preferential not to an individual's degree, i.e., how many people has he/she collaborated with, but to his/her facet degree, i.e., how many maximal groups or facets has he/she collaborated within. Based on our observation that several real-world facet size distributions have significant deviation from power law-mainly since larger facets tend to subsume smaller ones-we adopt a data-driven approach. We prove that the facet degree distribution yielded by GENESCs is power law distributed for large SCs and show that it is in agreement with real world co-authorship data. Finally, based on our intuition of collaboration formation in domains such as collaborative scientific experiments and movie production, we propose two variants of GENESCs based on clamped and hybrid preferential attachment schemes, and show that they perform well in these domains.