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We consider the triangular lattice ice model (20-Vertex model) with fourtypes of domain-wall type boundary conditions. In types 1 and 2, theconfigurations are shown to be equinumerous to the quarter-turn symmetricdomino tilings of an Aztec-like holey square, with a central cross-shaped hole.The proof of this statement makes extensive use of integrability and of aconnection to the 6-Vertex model. The type 3 configurations are conjectured tobe in same number as domino tilings of a particular triangle. The fourenumeration problems are reformulated in terms of four types of AlternatingPhase Matrices with entries 0 and sixth roots of unity, subject to suitablealternation conditions. Our result is a generalization of the ASM-DPPcorrespondence. Several refined versions of the above correspondences are alsodiscussed.

Twenty-Vertex model with domain wall boundaries and domino tilings