The growth of single ice crystals from supercooled heavy water was studied under microgravity conditions in the Japanese Experiment Module "KIBO" of the International Space Station (ISS). The velocities of dendrite tips parallel to the a axis and the growth rates of basal faces parallel to the c axis were both analyzed under supercooling ranging from 0.03 to 2.0 K. The velocities of dendrite tips agree with the theory for larger amounts of supercooling when the growth on the basal faces are not zero. At very low supercooling there is no growth on the basal faces. With increasing supercooling the basal faces start to grow, the growth rate changing as a function of supercooling with a power law with an exponent of about 2, with the exponent approaching 1 as supercooling increases further. We interpret the growth on the basal faces as being controlled by two-dimensional nucleation under low supercooling, with a change in the growth kinetics to spiral growth with the aid of screw dislocations with increasing supercooling then to a linear growth law. We discuss the combined effect of tip velocity and basal face kinetics on pattern formation during the growth of ice.