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We present a single, connected tile which can tile the plane but onlynon-periodically. The tile is hexagonal with edge markings, which impose simplerules as to how adjacent tiles are allowed to meet across edges. The first ofthese rules is a standard matching rule, that certain decorations match acrossedges. The second condition is a new type of matching rule, which allows tilesto meet only when certain decorations in a particular orientation are given theopposite charge. This forces the tiles to form a hierarchy of triangles,following a central idea of the Socolar--Taylor tilings. However, the newedge-to-edge orientational matching rule forces this structure in a verydifferent way, which allows for a surprisingly simple proof of aperiodicity. Weshow that the hull of all tilings satisfying our rules is uniquely ergodic andthat almost all tilings in the hull belong to a minimal core of tilingsgenerated by substitution. Identifying tilings which are charge-flips of eachother, these tilings are shown to have pure point dynamical spectrum and aregular model set structure.

An aperiodic tile with edge-to-edge orientational matching rules