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Rechargeable aluminum-ion batteries are promising in high-power density but still face critical challenges of limited lifetime, rate capability, and cathodic capacity. We design a "trihigh tricontinuous" (3H3C) graphene film cathode with features of high quality, orientation, and channeling for local structures (3H) and continuous electron-conducting matrix, ion-diffusion highway, and electroactive mass for the whole electrode (3C). Such a cathode retains high specific capacity of around 120 mAh g-1 at ultrahigh current density of 400 A g-1 (charged in 1.1 s) with 91.7% retention after 250,000 cycles, surpassing all the previous batteries in terms of rate capability and cycle life. The assembled aluminum-graphene battery works well within a wide temperature range of -40 to 120°C with remarkable flexibility bearing 10,000 times of folding, promising for all-climate wearable energy devices. This design opens an avenue for a future super-batteries. [ABSTRACT FROM AUTHOR]