When selecting a particular type of dielectric resonators for certain applications, it is important to have a possibility to analyze their comparative performance and other characteristics. Unfortunately, this task is rather complicated due to contradictions between some quality factors.A distinctive feature of dielectric resonators as oscillating systems is their multimode nature. The quality factor (Q-factor) of these resonators may be enhanced when operated at higher modes, however at the expense of such an important characteristic as the density (number) of resonant modes. The situation can be improved with the use of special mode-selection procedures. Variation of the selective properties is realized by additional external and internal structural elements introduction into resonator construction. These elements selectively influence the intensity of different modes [l].The selectivity is greatly dependent upon resonator form and medium dielectric permeability. Because of this, a study of the selective properties of resonators having differing forms is particularly important.It's essential to know the number of high-Q modes for investigation of the selective properties of dielectric resonators. We have solved this problem for resonators in the form of three-dimensional periodic kaleidoscopes.When selecting a research method, one should take into consideration the symmetry properties of these kaleidoscopes and the spaces generated by them. Based on these properties, it is possible to construct a system of equivalent points and directions in each kaleidoscope using mirror images method. According to method of partial plane waves, each direction is related to a plane wave, and kaleidoscopic domain is associated with the solution of Maxwell equations as superposition of plane waves. Such solutions are used in studies of the diffraction phenomena in kaleidoscopic structures, mode fields and selective properties of waveguides and resonators.Consider a prism-shaped resonator. The form of the resonator is a regular prism having 0 I z I 1 in length, and prism underlying equicathetus triangle sizes are x and y such that 0 I y S x I a . Such resonator is characterized bythe outward-drawn normals to the faces rZ,(*) = {o,o, +1}, n, = (0, -1, o}, n4 = {l, 0, o}, n, = ---, 0 , (1) ( :7: ) -and relative dielectric permeability E > 1. The modes of a same form perfect resonator are represented as a superposition of 16 plane waves [2] having wave vectors for all sign combinations of x, y , z components. Partial waves of other kaleidoscopic resonators are described in [Wl.High-Q modes are formed in case of the total (or nearly total) reflection of partial waves from the resonator faces. This results in inequalities limiting wave-vector components values, and determines the phase space for the high-Q modes.The normalized density p of such modes is derived from the ratio of their phase volume and the phase volume of all the modes of the associated perfect resonator. The calculation is conveniently performed with a spherical coord...