▁eight ▁lines , ▁with ▁three ▁points ▁on ▁each ▁line ▁and ▁three ▁lines ▁through ▁each ▁point . ▁It ▁is ▁not ▁possible ▁to ▁draw ▁points ▁and ▁lines ▁having ▁this ▁pattern ▁of ▁inc id ences ▁in ▁the ▁E uclidean ▁plane , ▁but ▁it ▁is ▁possible ▁in ▁the ▁complex ▁project ive ▁plane . ▁ ▁Co ordinates ▁ ▁asked ▁whether ▁there ▁exists ▁a ▁pair ▁of ▁pol yg ons ▁with ▁p ▁sides ▁each , ▁having ▁the ▁property ▁that ▁the ▁vertices ▁of ▁one ▁polygon ▁lie ▁on ▁the ▁lines ▁through ▁the ▁edges ▁of ▁the ▁other ▁polygon , ▁and ▁vice ▁vers a . ▁If ▁so , ▁the ▁vertices ▁and ▁edges ▁of ▁these ▁pol yg ons ▁would ▁form ▁a ▁project ive ▁configuration . ▁For ▁ ▁there ▁is ▁no ▁solution ▁in ▁the ▁E uclidean ▁plane , ▁but ▁ ▁found ▁pairs ▁of ▁pol yg ons ▁of ▁this ▁type , ▁for ▁a ▁general ization ▁of ▁the ▁problem ▁in ▁which ▁the ▁points ▁and ▁edges ▁belong ▁to ▁the ▁complex ▁project ive ▁plane . ▁That ▁is , ▁in ▁Kant or ' s ▁solution , ▁the ▁coordinates ▁of ▁the ▁polygon ▁vertices ▁are ▁complex ▁numbers . ▁Kant or ' s ▁solution ▁for ▁, ▁a ▁pair ▁of ▁mut ually - ins cribed ▁quad ril ater als ▁in ▁the ▁complex ▁project ive ▁plane , ▁is ▁called ▁the ▁M ö b ius – K ant or ▁configuration . ▁▁ ▁supplies ▁the ▁following ▁simple ▁complex ▁project ive ▁coordinates ▁for ▁the ▁eight ▁points ▁of ▁the ▁M ö b ius – K ant or ▁configuration : ▁( 1 , 0 , 0 ), ▁( 0 , 0