| Summary: | Abstract The aim of this note is to present some new explicit examples of O(d, d)generalised Leibniz parallelisable spaces arising as the normal bundles of adjoint orbits O $$ \mathcal{O} $$ of some semi-simple Lie group G. Using this construction, an explicit expression for a generalised frame is given in the case when the orbits are regular, but subtleties arise when they become degenerate. In the case of regular orbits, the resulting space is a globally flat fiber bundle over O $$ \mathcal{O} $$ which can be made compact, allowing for a generalised Scherk-Schwartz reduction. This means these spaces should admit consistent supergravity truncations. For degenerate orbits, the procedure hinges on the existence of a suitable metric, allowing for a consistent normalisation of the generalised frame.
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