  Thermodynamics places a limit on the efficiency of heat engines, but not on
their output power or on how the power and efficiency change with the engine's
cycle time. In this manuscript, we develop a geometrical description of the
power and efficiency as a function of the cycle time, applicable to an
important class of heat engine models. This geometrical description is used to
design engine protocols that attain both the maximal power and maximal
efficiency at the fast driving limit. Furthermore, using this method we also
prove that no protocol can exactly attain the Carnot efficiency at non-zero
power.
