The invention relates to an internal cone dental implant, of the type that is provided with a blind axial hole comprising a troncoconical section having on its closed end an internally threaded area, designed to receive a dental prosthesis that is adapted to be solidly secured to the head of the implant. The blind axial hole comprises a polygonal prismatic section circumscribed inside the troncoconical section, which is adapted to position and fix the orientation of the prosthesis in relation to the implant, and the outside of the head of the implant comprises a first prismatic end section followed by a second troncoconical section inside which the first section is inscribed, forming an outer support area of the prosthesis. The invention also relates to an assembly consisting of a dental implant, a morphological auxiliary piece and a prosthesis.