In the present Letter, we investigate a spherical hohlraums with octahedral six laser entrance holes (LEHs) for inertial fusion, which has advantages over the conventional hohlraums of cylindrical geometry since it contains only one cone at each LEH and the problems caused by the beam overlap and crossed-beam energy transfer can be eliminated and the backscattering can be reduced. In particular, our study indicates that at a specific hohlraum-to-capsule radius ratio, i.e., the golden ratio, the flux asymmetry on capsule can be significantly reduced. From our study, this golden octahedral hohlraum has robust high symmetry, low plasma filling and low backscattering. Though the golden octahedral hohlraum needs 30% more laser energy than traditional cylinder for producing the ignition radiation pulse of 300 eV, it is worth for a robust high symmetry and low backscattering. The proposed octahedral hohlraum is also flexible and can be applicable to diverse inertial fusion drive approaches. As an application, we design an ignition octahedral hohlraum for the hybrid drive.PACS numbers: 52.70. La, 52.35.Tc, 47.40.Nm Introduction-The hohlraum is crucial for the inertial fusions of both indirect drive [1][2][3] and the hybrid indirectdirect drive proposed recently (HID) [4]. In the indirect drive approach, the hohlraum is first heated by laser beams to a few million Kelvin and then the energy flux of the transferred X-ray radiation compress the deuterium-tritium capsule at a convergence ratio of 25 to 45, making the nuclear fuel finally burn in a self-sustained way. In the corresponding hohlraum design, the hohlraum shape, size and the number of Laser Entrance Hole (LEH) are optimized to balance tradeoffs among the needs for capsule symmetry, the acceptable hohlraum plasma filling, the requirements for energy and power, and the laser plasma interactions. Among many requirements, the energy coupling and flux symmetry are of most concerned. A higher energy coupling will economize the input energy and increase the fusion energy gain. More importantly, a very uniform flux from the hohlraum on the shell of capsule is mandatory because a small drive asymmetry of 1% [2] can lead to the failure of ignition. Actually, the small flux asymmetry will be magnified during the compression process due to the varied kinds of instabilities and results in a serious hot-cold fuel mixture that can dramatically lessen the temperature or density of the hot spot for ignition.Various hohlraums with different shapes have been proposed and investigated, such as cylinder hohlraum [1,2], rugby hohlraum [5-10] and elliptical hohlraum [11]. These hohlraums are elongated with a length-to-diameter ratio greater than unity and have cylindrically symmetry with two LEHs on the ends. Among all above hohlraums, the cylindrical hohlraums are used most often in inertial fusion studies and are chosen as the ignition hohlraum on NIF [3,12,13], though it breaks the spherical symmetry and leads to cross coupling between the modes.Intuitively, spherical hohlraum h...