▁higher ▁symmetry , ▁the ▁regular ▁and ▁qu as ire g ular ▁poly hed ra . ▁Some ▁later ▁authors ▁prefer ▁to ▁say ▁that ▁these ▁are ▁not ▁sem ire g ular , ▁because ▁they ▁are ▁more ▁regular ▁than ▁that ▁- ▁the ▁uniform ▁poly hed ra ▁are ▁then ▁said ▁to ▁include ▁the ▁regular , ▁qu as ire g ular ▁and ▁sem ire g ular ▁ones . ▁This ▁naming ▁system ▁works ▁well , ▁and ▁recon c iles ▁many ▁( but ▁by ▁no ▁means ▁all ) ▁of ▁the ▁conf us ions . ▁ ▁In ▁practice ▁even ▁the ▁most ▁em inent ▁authorities ▁can ▁get ▁themselves ▁confused , ▁defining ▁a ▁given ▁set ▁of ▁poly hed ra ▁as ▁sem ire g ular ▁and / or ▁Arch im ede an , ▁and ▁then ▁assuming ▁( or ▁even ▁stating ) ▁a ▁different ▁set ▁in ▁subsequent ▁discuss ions . ▁Assuming ▁that ▁one ' s ▁stated ▁definition ▁applies ▁only ▁to ▁convex ▁poly hed ra ▁is ▁probably ▁the ▁most ▁common ▁failing . ▁C ox eter , ▁C rom well ▁and ▁C und y ▁& ▁Rol lett ▁are ▁all ▁guilty ▁of ▁such ▁sli ps . ▁ ▁General ▁remarks ▁ ▁In ▁many ▁works ▁sem ire g ular ▁poly hed ron ▁is ▁used ▁as ▁a ▁syn onym ▁for ▁Arch im ede an ▁solid . ▁For ▁example , ▁C und y ▁& ▁Rol lett ▁( 1 9 6 1 ). ▁ ▁We ▁can ▁distinguish ▁between ▁the ▁fa cially - regular ▁and ▁vertex - trans itive ▁figures ▁based ▁on ▁G os set , ▁and ▁their ▁vert ically - regular ▁( or