Symbolic Representation of Surfaces

When a surface is represented symbolically, it is made into a polygonal shape with different edges labelled by different letters. If the same letter is repeated, it means the corresponding edge is traversed twice. Each edge is also labelled with an arrow to indicate how the edges are joined up - the edges are joined in the directions of the arrows, so that if the arrows on edges labelled a both point up, the edges labelled are joined by folding the polginal shape and if the edges point in opposite direction - one up and one down - then the shape is given a half twist before the edges are joined up.




Klein Bottle

Real Projective Plane or


Mobius Strip