Geodesic
The geometry of ideal 2-dimensional simplicial complexes
Glasgow mathematical journal, Tome 43 (2001) no. 1, pp. 39-66

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In this paper, we study geometric structures on 2-dimensional simplicial complexes. In particular, we consider hyperbolic structures and measured foliations on these simplicial complexes. We describe the spaces of such structures and we relate the two resulting spaces in a manner which is analogous to Thurston's compactification of the Teichmüller space of a surface. 
Charitos, Charalampos; Papadopoulos, Athanase. The geometry of ideal 2-dimensional simplicial complexes. Glasgow mathematical journal, Tome 43 (2001) no. 1, pp. 39-66. doi: 10.1017/S0017089501010059
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