© Copyright © 2019 Sen and Mason. A variation of the topological constraint theory is proposed where an atomic network is modeled as a collection of rigid polytopes, and which explicitly distinguishes the bond angle constraints as well as rigid bond angles from flexible ones. The proposed theory allows for direct quantitative estimation of the fraction f of zero-frequency or floppy modes of the network. A preliminary model is proposed to connect the theory to the two key experimental observables that characterize glass-forming liquids, i.e., the glass transition temperature Tg and fragility m. The predicted values are tested against the literature data available for binary and ternary chalcogenides in the Ge-As-Se system. The Tg is related to f in this model by the activation entropy associated with the bond scission-renewal dynamics that is at the heart of transport and relaxation in glass-forming liquids. On the other hand, the large and temperature-dependent conformational entropy contribution of the 1-polytopes, i.e., the selenium chain elements in these chalcogenide glass-forming liquids, plays a key role in controlling the variation of m with f.