Among various energy storage devices, flexible supercapacitors having high mechanical stability with extreme bending and foldable features are highly attractive for a large number of emerging portable lightweight consumer devices. Here, we report the fabrication of such a superflexible supercapacitor by using novel octahedron-shaped NiCo2O4 nanoparticles as the electrode material for the first time. A new, low-cost hydrothermal method was used to synthesize 50-60 nm monodispersed perfect octahedron nanoparticles without any structural deformation. An all-solid-state symmetric flexible supercapacitor was fabricated by sandwiching the octahedron nanoparticles and [EMIM][BF4] ionic liquid electrolyte between two sheets of newly developed superflexible current collector substrate. The calculated specific capacity and specific capacitance values are found to be 97.9 mAh g-1 and 117.3 F g-1, respectively, at 0.625 A g-1 current density and 3.0 V applied potential. It also offered a high energy density value of 33.54 Wh kg-1 and 10 000 measured cycling stability. The supercapacitor is so flexible that it can be bent or fold up to 180° without any mechanical deformation, and the measured capacitance and energy and power densities remain almost constant at any angle of twisting. For instance, calculated values of capacitances obtained by bending the cell at angles of 180, 150, 135, 90, and 45° are found to be 62, 63.3, 63.73, 64, and 66 F g-1 respectively, in comparison to 67 F g-1 for a nonbending or flat (0°) cell. A faster ion switching between electrode/electrolyte interface, [EMIM][BF4] electrolyte, and octahedron shape of the nanoparticle electrode material is found to be responsible for the outstanding charge storage behavior.