▁vertex - trans itive . ▁ ▁Since ▁G os set , ▁other ▁authors ▁have ▁used ▁the ▁term ▁sem ire g ular ▁in ▁different ▁ways ▁in ▁relation ▁to ▁higher ▁dimensional ▁poly top es . ▁E . ▁L . ▁El te ▁ ▁provided ▁a ▁definition ▁which ▁C ox eter ▁found ▁too ▁artificial . ▁C ox eter ▁himself ▁dub bed ▁G os set ' s ▁figures ▁uniform , ▁with ▁only ▁a ▁quite ▁restricted ▁subset ▁class ified ▁as ▁sem ire g ular . ▁ ▁Yet ▁others ▁have ▁taken ▁the ▁opposite ▁path , ▁categor ising ▁more ▁poly hed ra ▁as ▁sem ire g ular . ▁These ▁include : ▁Three ▁sets ▁of ▁star ▁poly hed ra ▁which ▁meet ▁G os set ' s ▁definition , ▁analog ous ▁to ▁the ▁three ▁convex ▁sets ▁listed ▁above . ▁The ▁du als ▁of ▁the ▁above ▁sem ire g ular ▁sol ids , ▁arg uing ▁that ▁since ▁the ▁dual ▁poly hed ra ▁share ▁the ▁same ▁symmet ries ▁as ▁the ▁original s , ▁they ▁too ▁should ▁be ▁regarded ▁as ▁sem ire g ular . ▁These ▁du als ▁include ▁the ▁Catal an ▁sol ids , ▁the ▁convex ▁di py ram ids ▁and ▁ant id ip y ram ids ▁or ▁tra pez oh ed ra , ▁and ▁their ▁non con vex ▁analog ues . ▁ ▁A ▁further ▁source ▁of ▁confusion ▁lies ▁in ▁the ▁way ▁that ▁the ▁Arch im ede an ▁sol ids ▁are ▁defined , ▁again ▁with ▁different ▁interpret ations ▁appearing . ▁ ▁G os set ' s ▁definition ▁of ▁sem ire g ular ▁includes ▁figures ▁of