<p>Pyramidal solitons (solitons with more than two inflection points) of the generalized Korteweg–de Vries (KdV) equation are investigated. Necessary and sufficient conditions for the existence of such structures are presented. Within the framework of the generalized Gardner equation — the simplest model that admits pyramidal solitons as solutions — it is shown that these solutions are unstable. Numerical simulations of the evolution of initial perturbations close to pyramidal solitons are carried out. Depending on the type of perturbation, the pyramidal soliton either decays into a thick and a thin soliton, or into a thick soliton and dispersive tails. An example of an equation whose solutions include stable pyramidal solitons is given. Calculations of soliton interactions are also presented for models that allow pyramidal soliton type solutions.</p>