Kazakh traditional national ornament traces its origins back to ancient times as a heritage of Bronze Age cultures. And although the original mythological-sacral meaning of ornament patterns is lost or significantly distorted, but the importance of ornamental art in the worldview and everyday life of the people is significant. Due to this, the national ornament provides an opportunity to trace the process of ethnogenesis of the people and highlight its ethnographic features. Mathematical methods of ornament research began to be applied only at the end of the last century and demonstrated quite high efficiency in analyzing the structure of ornament. In this work, unlike the previous ones, a comprehensive study of the motif and the basis of the ornament - the grid, or lattice, on which it is built. The research methodology is based on the application of the laws of symmetry, in particular, the Curie principle. The object of the study was the national Kazakh felt carpet. It is shown that with the change of ornamentation the semantics of its content also changes. The analysis of motifs and border of the ornament was carried out, the grids on which they are created were established. The correspondence of the location of the types of ornamental elements with special points on the grid, having specific symmetrical properties in comparison with the whole ornamental field, is established. The role of invisible substrate (grid, lattice) for the construction of ornaments is confirmed.