In an effort to understand the structure property relationship in magnetically frustrated systems, an orthorhombic analog of the S = 1/2 Re-based oxide Li4MgReO6 has been successfully synthesized and its physical properties were investigated. Li4MgReO6 had been previously synthesized in a monoclinic system in an ordered NaCl structure type. That system was shown to exhibit spin glass behavior below similar to 12 K. The crystal structure of the latter phase was determined using powder X-ray diffraction data. A structural model was refined in the orthorhombic Fddd space group that resulted in cell dimensions of a = 5.84337 (7) angstrom, b = 8.33995 (9) angstrom, and c = 17.6237 (2) angstrom. The magnetic ions, Re6+ (S = 1/2), consist of various arrangements of interconnected triangles and trigonal prisms that offer potential for geometric magnetic frustration. Temperature dependent magnetic susceptibility reveals an AFM transition below similar to 2K along with a ZFC/FC divergence suggestive of spin freezing. The Curie-Weiss fitting parameters to the paramagnetic regime result in theta = -124 (1) K, which is indicative of predominant AFM interactions. A frustration index of, similar to 62 is in accordance with a highly frustrated magnetic ground state. Zero field (ZF) mu SR data provides evidence for the onset of magnetic order below 4 K, along with the evidence for dynamical fluctuations up to 5 K. Moreover, longitudinal field (LF) mu SR data reveals a complete decoupling in applied field at 2 K, which is indicative of static order in most or all of the volume fraction at similar to 2 K, with partial ordered volumes coexisting with dynamical fluctuations up to 5 K. Estimates of the relative strengths of various magnetic exchange pathways at the level of spin-dimer analysis for this novel system are calculated and are compared to those of the previously reported values for the monoclinic analog.