  In this study, we explore the influence of the helicity of the magnetic
axis-defined as the self-linking number of the curve-on the quality of
quasi-isodynamic stellarator-symmetric configurations constructed using the
near-axis expansion method (Camacho Mata et al. 2022; Plunk et al. 2019). A
class of magnetic axes previously unexplored within this formalism is
identified when analyzing the axis shape of the QIPC configuration (Subbotin et
al. 2006): the case of half-helicity (per field period). We show these shapes
are compatible with the near-axis formalism and how they can be used to
construct near-axis stellarators with up-to 5 field-periods, $\epsilon_{eff}
\approx$ 1.3%, and similar rotational transform as existing conventionally
optimized designs, without the need of a plasma boundary optimization.
