  Red blood cells flowing through capillaries assume a wide variety of
different shapes owing to their high deformability. Predicting the realized
shapes is a complex field as they are determined by the intricate interplay
between the flow conditions and the membrane mechanics. In this work we
construct the shape phase diagram of a single red blood cell with a
physiological viscosity ratio flowing in a microchannel. We use both
experimental in-vitro measurements as well as 3D numerical simulations to
complement the respective other one. Numerically, we have easy control over the
initial starting configuration and natural access to the full 3D shape. With
this information we obtain the phase diagram as a function of initial position,
starting shape and cell velocity. Experimentally, we measure the occurrence
frequency of the different shapes as a function of the cell velocity to
construct the experimental diagram which is in good agreement with the
numerical observations. Two different major shapes are found, namely croissants
and slippers. Notably, both shapes show coexistence at low (<1 mm/s) and high
velocities (>3 mm/s) while in-between only croissants are stable. This
pronounced bistability indicates that RBC shapes are not only determined by
system parameters such as flow velocity or channel size, but also strongly
depend on the initial conditions.
