Give an expression for the pattern inventory of 2colorings o

Give an expression for the pattern inventory of 2-colorings of the edges of the unoriented figure on the right (rotations and Hips allowed).

Solution

It is basically one-thrd of a rectagular cubiod. The volume of a rectagular cubiod is 2*(lb+bh+lh). As such the expression of the figure can be written as

f(x,y,z) = (2/3)*(xy+yz+zx)