TRIPLET solves the two-dimensional multigroup transport equation in planar geometries by using a regular triangular mesh. Regular and adjoint, inhomogeneous and homogeneous (K/sub eff/ and eigenvalue searches) problems subject to vacuum, reflective, or source boundary conditions are solved. General anisotropic scattering ia allowed, and anisotropic distributed sources are permitted. The discrete ordinates approximation is used for the angular variables. A finite element method in which the angular flux is assumed to be given by a low-order polynomial in each triangle is used to solve the discrete ordinates equations. Angular fluxes are allowed to be discontinuous across triangle boundaries. A six-group, S/sub 2/, 1700-triangle, k/sub eff/ calculation of an EBR-II core requires about 4.4 minutes of CDC-7600 time; running times vary almost linearly with the total number of unknowns. Sources, fluxes, S/sub n/ constants, and cross sections may be read from standard interface files; flexible edit options are provided. Six scratch units and two system I/O units are required. A large bulk memory is necessary if core storage is inadequate. This program is operational on the CDC-7600, CDC-6600, and IBM- 360/195 computers. (13 figures, 13 tables) (RWR)