 In simpler terms, the value of an orientable surface's genus is equal to the number of "holes" it has.The non-orientable genus, demigenus, or Euler genus of a connected, non-orientable closed surface is a positive integer representing the number of cross-caps attached to a sphere.Alternatively, it can be defined for a closed surface in terms of the Euler characteristic χ, via the relationship χ = 2 − "k", where "k" is the non-orientable genus.