Refractive index (RI) measurements, depolarized collision-induced light (CILS) scattering and ab initio quantum chemical calculations are used to determine the dipole (alpha), dipole-quadrupole (A), and dipole-octopole polarizability (E) of adamantane, C10H16. For this molecule of symmetry group T-d the three polarizabilities can be represented by a single scalar quantity. From experiment we obtain for the static dipole polarizability at T approximate to 400-500 K 107.5 +/-1.1 e(2)a(0)(2)E(h)(-1), and for the higher polarizabilities \A \ =102.0 +/-7.8 e(2)a(0)(3)E(h)(-1), and \E oe =720 +/- 80 e(2)a(0)(4)E(h)(-1). We have performed conventional ab initio and density functional theory calculations with specifically designed basis sets. A very large [4s3p3d1f/3s2p1d] basis set consisting of 574 basis functions is thought to provide near-Hartree-Fock values for alpha ,A and E: alpha =101.72 e(2)a(0)(2)E(h)(-1), A=-6.5 e(2)a(0)(3)E(h)(-1), and E=-71.0 e(2)a(0)(4)E(h)(-1). Our final theoretical estimates for these properties are alpha =107.5 +/-1.0 e(2)a(0)(2)E(h)(-1), A=-8.0 +/-1.5 e(2)a(0)(3)E(h)(-1), and E=-76.5 +/-5.5 e(2)a(0)(4)E(h)(-1). Very strong electron correlation effects are found for both the first (beta) and second (gamma) hyperpolarizability. Our estimate for beta equivalent to beta (xyz) and the mean <()over bar> are 41.4 +/-5.6 e(3)a(0)(3)E(h)(-2) and (25 +/-2)x10(3) e(4)a(0)(4)E(h)(-3), respectively. For the octopole and hexadecapole moments we propose Omega=-4.4 +/-0.2 ea(0)(3) and Phi=-100.8 +/-5.5 ea(0)(4). The basis sets constructed in this work should provide reliable computational tools for the study of intermolecular interactions of adamantane.