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Patients who have undergone surgical hemi/segmental/subtotal mandibulectomy for various reasons with resulting mandibular deviation are given a guide flange. If secondary osseous grafting is planned, the doctor must wait for the graft, lesion, or radiotherapeutic effects to resolve. A definitive prosthesis can be planned only when the graft has been healed. During this time lag, the patient must be fitted with a prosthesis to rectify mandibular deviation caused by unilateral muscle strain. Furthermore, in some circumstances, a definitive prosthesis must be postponed due to bone grafting failure or the patient's unwillingness to undergo a second surgery. This clinical case report shows a mandibular guide flange prosthesis fabricated for a patient.

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Chari and Greenstein [Adv. Math. 2009] introduced certain combinatorial subsets of the roots of a finite-dimensional simple Lie algebra g, which were important in studying Kirillov-Reshetikhin modules over Uq( g) and their specializations. Later, Khare [J. Algebra. 2016] studied these subsets for large classes of highest weight g-modules (in finite type), under the name of weak-A-faces for a subgroup A of (R, +) , and more generally, ({2}; {1, 2})-closed subsets. These notions extend and unify the faces of Weyl polytopes as well as the aforementioned combinatorial subsets.In this paper, we consider these 'discrete' notions for an arbitrary Kac-Moody Lie algebra g, in four distinguished settings: (a) the weights of an arbitrary highest weight g-module V ; (b) the convex hull of the weights of V ; (c) the weights of the adjoint representation; (d) the roots of g. For (a) respectively, (b) for all highest weight g-modules V , we show that the weak-A-faces and ({2}; {1, 2})-closed subsets agree, and equal the sets of weights on exposed faces (respectively, equal the exposed faces) of the convex hull of weights conv R wtV . This completes the partial progress of Khare in finite type, and is novel in infinite type. Our proofs are type-free and self-contained.For (c) and (d) involving the root system, we similarly achieve complete classifications. For all Kac-Moody g-interestingly, other than sl3(C), sl3(C)-we show the weak-A-faces and ({2}; {1, 2})closed subsets agree, and equal Weyl group translates of the sets of weights in certain 'standard faces' (which also holds for highest weight modules). This was proved by Chari and her coauthors for root systems in finite type, but is novel for other types.