Cagelike carbon frameworks, characterized by robust covalent bonding and unique topological motifs, offer a fertile ground for the discovery of high-temperature superconductors under ambient conditions. Inspired by Archimedean polyhedral geometry, we propose a carbon cage structure, ${\mathrm{C}}_{48}$, featuring cubic symmetry and dynamic stability at ambient pressure. Leveraging this framework, we applied a guest-host engineering approach to systematically explore 961 binary and ternary compounds of the form $XY{\mathrm{C}}_{24}$ via high-throughput density functional theory calculations, in which the guest elements $X$ and $Y$ are located at the cage corners and body center, respectively. Through stringent stability and metallicity screening, we identified 123 compounds that are both dynamically stable and metallic at ambient pressure, all of which exhibit intrinsic superconductivity. Notably, our analysis reveals a necessary correlation between the dynamical stability of these compounds and the atomic radius of the guest atoms, highlighting the critical role of size compatibility in stabilizing the host-guest framework. Moreover, five of these superconductors exhibit critical temperatures ($T_c$) exceeding the McMillan limit. Among them, ${\mathrm{NaRbC}}_{24}$ and ${\mathrm{TlKC}}_{24}$ demonstrate ideal superconducting properties, with $T_c$ reaching as high as 70.7 and 75.2 K, respectively. The high $T_c$ originates from strong electron-phonon coupling driven by pronounced Fermi surface nesting and carbon-dominated electronic states at the Fermi level. Our findings highlight the critical role of guest atom size in stabilizing the structure and enhancing superconductivity. This work not only enriches the family of carbon-based superconductors but also establishes polyhedral cage design as a powerful paradigm for the targeted discovery of ambient-pressure high-temperature superconductors.

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• Crystal structure
• Superconductivity
• Carbon-based materials
• Superconductors
• BCS theory
• First-principles calculations