Context. The near-Earth asteroid (3200) Phaethon is an intriguing object: its perihelion is at only 0.14 au and is associated with the Geminid meteor stream. Aims: We aim to use all available disk-integrated optical data to derive a reliable convex shape model of Phaethon. By interpreting the available space- and ground-based thermal infrared data and Spitzer spectra using a thermophysical model, we also aim to further constrain its size, thermal inertia, and visible geometric albedo. Methods: We applied the convex inversion method to the new optical data obtained by six instruments and to previous observations. The convex shape model was then used as input for the thermophysical modeling. We also studied the long-term stability of Phaethon's orbit and spin axis with a numerical orbital and rotation-state integrator. Results: We present a new convex shape model and rotational state of Phaethon: a sidereal rotation period of 3.603958(2) h and ecliptic coordinates of the preferred pole orientation of (319°, -39°) with a 5° uncertainty. Moreover, we derive its size (D = 5.1 ± 0.2 km), thermal inertia (Γ = 600 ± 200 J m-2 s-1/2 K-1), geometric visible albedo (pV = 0.122 ± 0.008), and estimate the macroscopic surface roughness. We also find that the Sun illumination at the perihelion passage during the past several thousand years is not connected to a specific area on the surface, which implies non-preferential heating.