[en] A newly developed triangular polynomial expansion nodal method (TRIPEN) for solving the multi-group diffusion equation is presented. This new method improves on the previous triangle-based polynomial expansion nodal method (TPEN) for hexagonal core analysis by explicitly treating the six triangles within the node as the homogenized region. The TRIPEN method provides more versatility for the neutronics treatment of the hexagonal assembly of the prismatic HTR which has large off center circular control rod regions. The TRIPEN method results in a linear system of equations for the one node problem which is considerably simpler than TPEN.. The new method, TRIPEN, is compared to the performance of the previous method, TPEN using both hexagonal and triangular based cross sections. A reference transport solution for a 2-D seven hexagon (assembly) VHTR-like problem is solved using the HELIOS lattice physics code. Each method is used to predict the control rod worth of the system, where the central assembly contains the control rod. Cross sections for the nodal methods are generated based on single assembly and seven assembly models to better understand the source of errors. Overall TRIPEN shows very good agreement with the HELIOS transport solution, predicting a rod worth that is ∼240 pcm Δρ different from the transport solution when using discontinuity factors, while TPEN predicts a rod worth 1145 pcm Δρ different from the transport solution. (authors)