In previous studies, acoustical levitation in the far-field was limited to particles. Here, this paper proposes the "boundary hologram method," a numerical design technique to generate a static and stable levitation field for macroscopic non-spherical rigid bodies larger than the sound wavelength λ. This paper employs boundary element formulation to approximate the acoustic radiation force and torque applied to a rigid body by discretizing the body surface, which is an explicit function of the transducer's phase and amplitude. Then, the drive of the phased array is numerically optimized to yield an appropriate field that stabilizes the body's position and rotation. In experiments, this paper demonstrates the levitation in air of an expanded polystyrene sphere with a diameter of 3.5 λ and a regular octahedron with diagonal length of 5.9 λ, both located 24 λ from the acoustic elements, by a 40 kHz (λ = 8.5 mm) ultrasonic phased array. This method expands the variety of objects that can be levitated in the far-field of an ultrasonic phased array.