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As an advanced amorphous material, sp³ amorphous carbon exhibits exceptional mechanical, thermal and optical properties, but it cannot be synthesized by using traditional processes such as fast cooling liquid carbon and an efficient strategy to tune its structure and properties is thus lacking. Here we show that the structures and physical properties of sp³ amorphous carbon can be modified by changing the concentration of carbon pentagons and hexagons in the fullerene precursor from the topological transition point of view. A highly transparent, nearly pure sp³−hybridized bulk amorphous carbon, which inherits more hexagonal-diamond structural feature, was synthesized from C₇₀ at high pressure and high temperature. This amorphous carbon shows more hexagonal-diamond-like clusters, stronger short/medium-range structural order, and significantly enhanced thermal conductivity (36.3 ± 2.2 W m−1 K−1) and higher hardness (109.8 ± 5.6 GPa) compared to that synthesized from C₆₀. Our work thus provides a valid strategy to modify the microstructure of amorphous solids for desirable properties.