We investigate the optical properties of a three-dimensional metamaterial nanotip that has a pyramidal shape. The nanotip itself is made of a large number of densely packed metallic nanospheres. In analogy to the emergence of a continuous energy band in a crystal, the strong coupling among neighboring nanospheres forces them to act collectively and allows the observation of a broad plasmonic band. The largely increased degrees of freedom within the metamaterial nanotip allow to sustain a great variety of different localized eigenmodes. In this contribution, we systematically reveal their peculiar polarization state and show that they allow for light localization in various well-defined spatial domains