Numerical simulations of multi-body systems involve evaluating the effect of interaction between different types of surfaces coming into contact. The application of contact constraints during the mechanically evolving phases of the problem has been an active area of research in recent decades. Second-order elements are used in finite element analysis to achieve higher accuracy than linear elements. Their ability to better capture surface curvature makes them more physically robust for determining contact traction than linear elements. This work presents a surface-to-surface algorithm for contact between bodies described by second-order hexahedral elements. While there have been formulations for surface-to-surface algorithms in the literature, they have preferential treatments for the contacting surfaces with the choice of master and slave surfaces [1]. The dual pass approach often employed to eliminate this biasing effect can be computationally expensive. For second-order elements, boundary facets having quadratic interpolation can be divided into sub-facets which are then used for establishing the contacting pairs among the neighbouring bodies [2]. With the use of a newly developed mid-plane approach between these sub-facets, interpenetration between the facets is established. By using a penalty method-based contact constraint in a single pass, normal traction between two facets can be evaluated. The regularized Coulomb's friction law considering the relative tangential velocity between the two facets provides the opposing forces for both stick and slip. The efficacy of the algorithm is shown through several benchmarks for different cases of contact conditions among solids. REFERENCES [1] Batistić, I., Cardiff, P., & Tuković, Ž. (2022). A finite volume penalty based segment-to-segment method for frictional contact problems. Applied Mathematical Modelling, 101, 673-693. [2] Puso, M. A., Laursen, T. A., & Solberg, J. (2008). A segment-to-segment mortar contact method for quadratic elements and large deformations. Computer methods in applied mechanics and engineering, 197(6-8), 555-566.