Hi I need to find a convex polytope that does not have a center. and by that i mean that is not centrally symmetrical. I am using an equilateral triangle as my example but I am having trouble proofing it.. Any help would be soooooooooooooooooo greatly appreciated because i have been trying to figure this out all weekend and just cant. all my work is wrong. i know that if something is centrally symmetrical than a reflection through a point r will give you the same figure back? right? i dont know. if somebody could walk me through a proof of this or get me started it would be great. i need to have this figured out by ten tonight.