The famed Klein Bottle

This is an unfamiliar view of the Klein bottle lifted from Ian Stewart. For a more familiar look, use the parametric version below

Think of it as a rectangle where one pair of opposite sides are joined directly, and the other pair are joined with a half twist. One sided surface first described by Felix Klein.

Polynomial form; Looks odd, from Ian Stewart.


Parametric form:

      x = cos(u)*(cos(u/2)*(sqrt_2+cos(v))+(sin(u/2)*sin(v)*cos(v)))
y = sin(u)*(cos(u/2)*(sqrt_2+cos(v))+(sin(u/2)*sin(v)*cos(v)))
z = -1*sin(u/2)*(sqrt_2+cos(v))+cos(u/2)*sin(v)*cos(v)

Figure 8 parametric form:
      x = (a+cos(uu/2)*sin(vv)-sin(uu/2)*sin(2*vv))*cos(uu)

      y = (a+cos(uu/2)*sin(vv)-sin(uu/2)*sin(2*vv))*sin(uu)

      z = sin(uu/2)*sin(vv)+cos(uu/2)*sin(2*vv)

Here is the PoV3-source I used
And here is the cat'ed figure 8 PoV3-source