I've been noticing a lot about opposites in the book and I think it's interesting how it often relates to male and female itneractions.
On page 409,
"...he [Mondaugen] seemed to look at fuel and oxidizer as paired opposites, male and female principles uniting in the mystical egg of the combustion chamber: creation and destruction, fire and water, chemical plus and chemical minus--."
"Valency," Pokler protested, "a condition of the outer shells, that's all."

Then on page 572 Andreas explains the importance of the mandala to Slothrop. It's a long paragraph so I won't type it all out, but basically there are two types of the letters on the mandala, male and female letters representing different directions. This came from the way that in their tribal villages, women and men lived on opposite sides of the village. The female letters represent fertilization, birth, breath, and soul, while the male letter represent activities, fire, preparation, and building, It says, "Each opposite pair of vanes worked together, and amoved in opposite senses. Opposites together."