Twinned dendrite growth has been found to occur in aluminum alloys when critical thermal conditions (G approximate to 100 K/cm, nu(s) approximate to 1 mm/s) and a slight convection in the melt are present during directional solidification. Split in their trunk by a coherent (111) twin plane, such dendrites grow along < 110 > directions with a complex branch structure of < 110 >, but also sometimes < 100 > secondary arms. To explain the twinned dendrite growth kinetics advantage, Eady and Hogan suggested that the Young Laplace equation involving the solid-liquid interfacial energy gamma(sl) and the twin energy gamma(t) at the triple junction stabilizes a grooved tip(1). Wood et al proposed instead that torque terms associated with the anisotropy of gamma(sl) stabilize a sharp pointed tip(2). Finally, Henry suggested the possibility of the existence of a doublon, initiated precisely by a grooved tip, that would evolve depending on the solute content(3). In a recent experimental work, we have shown that the doublon conjecture is probably not valid for high solute content aluminum alloys, whereas it could be valid at low, composition. In the present work, the twinned dendrite tip morphology and growth kinetics have been investigated using a 3D phase field method implemented on a massively parallel computer. The twin boundary energy has been imposed via an appropriate boundary condition fixing the angle of the phase field gradient with respect to the boundary. Besides this angle, various experimental conditions such as thermal gradient, gradient direction, velocity of the isotherms and compositions have been investigated. The growth kinetics obtained under such conditions has been compared with that of regular dendrites.