  A system of commutative hypercomplex numbers of the form w=x+hy+kz are
introduced in 3 dimensions, the variables x, y and z being real numbers. The
multiplication rules for the complex units h, k are h^2=k, k^2=h, hk=1. The
operations of addition and multiplication of the tricomplex numbers introduced
in this paper have a simple geometric interpretation based on the modulus d,
amplitude \rho, polar angle \theta and azimuthal angle \phi. Exponential and
trigonometric forms are obtained for the tricomplex numbers, depending on the
variables d, \rho, \theta and \phi. The tricomplex functions defined by series
of powers are analytic, and the partial derivatives of the components of the
tricomplex functions are closely related. The integrals of tricomplex functions
are independent of path in regions where the functions are regular. The fact
that the exponential form of the tricomplex numbers contains the cyclic
variable \phi leads to the concepts of pole and residue for integrals of
tricomplex functions on closed paths. The polynomials of tricomplex variables
can be written as products of linear or quadratic factors.
