Če je dana ▫$n_3$▫ konfiguracija, potem je eno-točkovna razširitev tehnika, ki iz nje konstruira ▫$(n + 1)_3$▫ konfiguracije. Konfiguracija je geometrijska, če se jo da realizirati s sestavom točk in ...premic v ravnini. Predstavimo metodo, ki dano geometrijsko ▫$n_3$▫ konfiguracijo z ravninsko koordinatizacijo njenih točk in premic najprej pretvori v ▫$(n + 1)_3$▫ konfiguracijo s pomočjo eno-točkovne razširitve, potem pa konstruira geometrijske realizacije teh ▫$(n + 1)_3$▫ konfiguracij. Pokažemo, da se da to storiti z uporabo samo homogenega kubičnega polinoma v samo treh spremenljivkah, neodvisnih od ▫$n$▫. To transformira računsko neobvladljiv problem v računsko obvladljiv problem.
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