  We report some minimal surfaces that can be seen as copies of a triply
periodic minimal surface (TPMS) related by reflections in parallel mirrors. We
call them minimal twin surfaces for the resemblance with twin crystal. Brakke's
Surface Evolver is employed to construct twinnings of various classical TPMS,
including Schwarz' Primitive (P) and Diamond (D) surfaces, their rhombohedral
deformations (rPD), and Schoen's Gyroid (G) surface. Our numerical results
provide strong evidences for the mathematical existence of D twins and G twins,
which are recently observed in experiment by material scientists. For rPD
twins, we develop a good understanding, by noticing examples previously
constructed by Traizet (2008) and Fujimori and Weber (2009). Our knowledge on G
twins is, by contrast, very limited. Nevertheless, our experiments lead to new
cubic polyhedral models for the D and G surfaces, inspired by which we
speculate new TPMS deformations in the framework of Traizet.
