An idea to develop a family of cellular cores for sandwich panels using a technology of prepreg folding is presented.Polar folded quadra-structures are regarded as a geometric basis for these cores whose standard fragment has the fourth degree of axial symmetry.The classification of the polar structures are described and a method of various quadra-structure synthesis is developed.A possibility to provide high strength of the structure due to preservation of faces reinforcement pattern is presented.Arrangement of the plane core on a bi-curvature surface is also introduced.Besides,provision of isotropy of the core in two or three directions are described.Finally,examples of cellular folded cores manufactured from basalt reinforced plastic are demonstrated. An idea to develop a family of cellular cores for sandwich panels using a technology of prepreg folding is presented. Polar folded quadra-structures are considered as a geometric basis for these cores whose standard fragment has the fourth degree of axial symmetry. The classification of the polar structures are described and a method of various quadra-structure synthesis is developed. A possibility to provide high strength of the structure due to preservation of faces reinforcement pattern is presented. Arrangement of the plane core on a bi-curvature surface is also introduced. Besides, provision of isotropy of the core in two or three directions are described. Finaally, examples of cellular folded cores manufactured from basalt reinforced plastic are demonstrated.