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We construct a new infinite family of ideal triangulations andH-triangulations for the complements of twist knots, using a method originatingfrom Thurston. These triangulations provide a new upper bound for the Matveevcomplexity of twist knot complements. We then prove that these idealtriangulations are geometric. The proof uses techniques of Futer and the secondauthor, which consist in studying the volume functional on the polyhedron ofangle structures. Finally, we use these triangulations to compute explicitlythe partition function of the Teichm\"uller TQFT and to prove the associatedvolume conjecture for all twist knots, using the saddle point method.

Geometric triangulations and the Teichm\"uller TQFT volume conjecture for twist knots