3D modelling and visualization based on general meshes needs a great amount of memory demands. Regular grids can substantially decrease them. Moreover, using the regular data structures results in efficient numerical procedures and simplicity of algorithms. On the other hand, disadvantage of regular grids is in lower flexibility of shape expression. One of the possibilities how to improve the shape expression of a regular grid is its decomposition to tetrahedra. The paper concerns  the problem which arises here -- nonconformity of decomposition.