Honeycomb structures under compression display illuminative geometrical patterns. As an example, Fig. 16.1(a) shows the so-called flower mode; a flowerlike pattern in (b), which is cut out from (a), comprises a regular hexagon and six identical cells surrounding this hexagon. Presented in (c) are its variants with different symmetries. In the numerical bifurcation analysis of the honeycomb structure to search for new patterns, it is pertinent to take advantage of group-theoretic analytical information.