The Gray's Kleinbottle was discovered by Albert Gray. These equations were taken from [Paul Bourke's webpage on Klein Bottles](http://paulbourke.net/geometry/klein/). To form a Gray's Kleinbottle, take a Möbius strip and attach its ends together, much like making a Möbius strip out of a plane.

The equations, adapted for use by the "XYZ Surface" generator from Blender's "Extra Objects" addon, are the following:

*x*: (a + cos(b*u/2.0) * sin(v) - sin(b*u/2.0) * sin(2*v)) * cos(c*u/2.0)

*y*: (a + cos(b*u/2.0) * sin(v) - sin(b*u/2.0) * sin(2*v)) * sin(c*u/2.0)

*z*: sin(b*u/2.0) * sin(v) + cos(b*u/2.0) * sin(2*v)

The parametric limitations are *u* from 0 to 4π; *v* from 0 to 2π.

Set the *a*, *b*, and *c* "helper functions" to customize the result. In the .blend file, the objects are named for their *a*, *b*, and *c* values (e.g., the object named GK_1.5_2_1 has *a*=1.5, *b*=2, and *c*=1).

Procedural rainbow texture included.