  Two-dimensional confinement of lattices produces a variety of order and
disorder phenomena. When the confining walls have atomic granularity, unique
structural phases are expected, of relevance in nanotribology, porous materials
or intercalation compounds where \textit{e.g.} electronic states can emerge
accordingly. The interlayer's own order is frustrated by the competing
interactions exerted by the two confining surfaces. We revisit the concept of
orientational ordering, introduced by Novaco and McTague to describe the twist
of incommensurate monolayers on crystalline surfaces. We predict a two-way
twist of the monolayer as its density increases. We discover such a behavior in
alkali atom monolayers (sodium, cesium) confined between graphene and an
iridium surface, using scanning tunneling microscopy and electron diffraction.
