The paper considers the triangle T7, which has seven nodes (three nodes in the points, three nodes in the middle of the sides and one node in the barycenter). It is shown that T7, as well as standard T10 can fulfill a dual role: both of a computational pattern and a finite element. Violation of inter-element continuity (incompatibility) at the boundary with triangular T6 or square Q8 has no undesirable effects. T7 model successfully withstands lump testing. Upon that the "blown" mode of T7 opens the possibility to generate by condensation many alternative models of T6 with different integral characteristics.

The paper considers new models of bases of serendipity finite elements (FE) Q8. In recent years, the library of serendipity finite elements has been significantly replenished with non-standard (alternative) models. The reasons for the inadequacy of the spectrum were identified and "recipes" were proposed to eliminate this shortcoming of standard serendipity models. New approaches to modeling bases with the help of hierarchical forms force to abandon conoids - linear surfaces that are associated with intermediate nodes of standard elements. Therefore, research is being conducted today, and it is not necessary to give up conoids. The paper shows how by compressing the surface of the conoid it is possible to obtain a mathematically sound and physically adequate spectrum of nodal loads.