some of your statement is wrongif you want just go through , no need to come back then can have one point with odd number of paths linking out... I think it's wrong. Make a simple example. 5 points in a straight line. got 2 points with odd number of path, right? From what I have known, to be a shape that can go through at once, it will have the property below. The point of odd number of paths linking out should be less than 2 or even number. However, not all the shapes fulfil this requirement can be a euler circle.