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We address the subject of transport in one-dimensional ballistic polygonloops subject to Rashba spin-orbit coupling. We identify the role played by thepolygon vertices in the accumulation of spin-related phases by studyinginterference effects as a function of the spin-orbit coupling strength. We findthat the vertices act as strong spin-scattering centers that hinder thedeveloping of Aharovov-Casher and Berry phases. In particular, we show that theoscillation frequency of interference pattern can be doubled by modifying theshape of the loop from a square to a circle.Comment: 4 pages, 4 figures. To appear in Phys. Rev.

Signatures of spin-related phases in transport through regular polygons