Abstract

AbstractWe introduce the multi-width of a lattice polytope and use this to classify and count all lattice tetrahedra with multi-width $$(1,w_2,w_3)$$ ( 1 , w 2 , w 3 ) . The approach used in this classification can be extended into a computer algorithm to classify lattice tetrahedra of any given multi-width. We use this to classify tetrahedra with multi-width $$(2,w_2,w_3)$$ ( 2 , w 2 , w 3 ) for small $$w_2$$ w 2 and $$w_3$$ w 3 and make conjectures about the function counting lattice tetrahedra of any multi-width.

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