Inverse carbon-free sandwich structures with formula E2P 4 (E=Al, Ga, In, Tl) have been proposed as a promising new target in main-group chemistry. Our computational exploration of their corresponding potential-energy surfaces at the S12h/TZ2P level shows that indeed stable carbon-free inverse-sandwiches can be obtained if one chooses an appropriate Group 13 element for E. The boron analogue B2P4 does not form the D4h-symmetric inverse-sandwich structure, but instead prefers a D2d structure of two perpendicular BP2 units with the formation of a double B-B bond. For the other elements of Group 13, Al-Tl, the most favorable isomer is the D4h inverse-sandwich structure. The preference for the D2d isomer for B2P 4 and D4h for their heavier analogues has been rationalized in terms of an isomerization-energy decomposition analysis, and further corroborated by determination of aromaticity of these species. Topsy turvy sandwiches: The possibility of the formation of inverse carbon-free sandwiches for clusters of type E2P4 with Group 13 elements B-Tl has been explored. This proposition is based on consideration of the aromaticity of the square-planar P4 2- unit, which should favor the formation of the cluster with a proper choice of the E + ions