The two-dimensional, stationary form of the equations of motion governing the flow in loosely coiled ducts of equilateral, triangular cross section are solved using a finite volume discretization procedure. The primary solution branch consists of a flow with two large, symmetrical streamwise vortices which are generated by the centrifugal force. Earlier works have investigated the formation of additional Moffat vortices near the corner of such ducts, driven by the secondary flow. Such corner vortices tend to be extremely weak in strength. When the outer wall is flat and one corner of the triangle points inwards, centrifugal instability gives rise to the formation of an additional pair of vortices near the center of the outer wall. Such four-cell solutions appear as dual solutions at the same Dean number, Dn, and the additional vortices are much stronger than the Moffat vortices. This phenomenon is very similar to those observed in the Dean problem for square and circular cross section. The four-cell solutions are found to be unstable to asymmetric perturbations. When the orientation of the triangular duct is changed such that the inner wall is flat such additional vortices do not form near the outer region of the duct and a unique two-cell solution that remains stable is obtained for Dean numbers as high as 350.