Triangular hyperbolic buildings
Riikka Kangaslampi, Alina Vdovina · arXiv (Cornell University) · 2005
We construct triangular hyperbolic polyhedra whose links are generalized 4-gons. The universal cover of those polyhedra are hyperbolic buildings, which appartments are hyperbolic planes tesselated by regular triangles with angles $π/4$. Moreover, the fundamental groups of the polyhedra acts simply transitively on vertices of the buildings.