Quaternions are spherical particles of three-dimensional space and possess two complementarysystems of coordinates. A quaternionic sphere, a conformal figure without centre, diameter and locality may be seen both as a material point and as an element of a wave. Physical movements can be described as motions of quaternionic spherical particles. In using linear vector coordinates a moved spherical quaternionic quantum may be seen as the motion of an elementary physical particle located at a point. Moved quaternionic quanta described by circular angle coordinates appear as elements of a wave. In seeing numbers of the Hamiltonian skew field as first elements of our natural space, physics possesses one new comprehensive model - free of contradictions - that comprises the classical duality of waves and particles.