I've actually read about 40 - 60% of this book before, it seems to be popular among editors to snip and prune some parts of this book to include in some anthology or other.
The basic story is this; America sends off 6 astronauts to the planet Alpha-Aleph orbiting around Alpha Centauri. The mastermind of the mission is Dr. Dieter von Knefhausen (of whom a German-er name there is none). So the Constitution, that's the ship, is supposed to take these 3 couples/astronauts/scientists/future colonists out to America's new hope in the stars. The trip takes quite some time to get there as may be imagined and Knefhausen has devised some activities for the crew to perform to relieve boredom. These activities are mostly "recreational" math problems only they're not recreational... *spoilers* they're actually the point of the whole trip, there is no planet Alpha-Aleph, it's all an elaborate hoax to try and generate new basic knowledge. Knefie (Dieter) tells it this way; "A Newton or Kant discovers a new island, and then the R&D people can build on it; but unless someone is is always discovering new islands, soon they have no place to build." *spoilers*
The mission then takes the turn to the bizarre: the crew starts to play around with the I-Ching, they tailor the drug that's supposed to control their sexual urges and ability to procreate into a mind altering hallucinogen, they start playing around with other states of consciousness, one of them even dies..but curiously doesn't...and well...shenanigans ensue.
If you've been buying and reading sci-fi anthologies from the past 20 years, chances are good that you've come across parts of this story, even those small parts are fun reads but I suggest you find a copy of this one as it is magnitudes more enjoyable as a whole. Compelling (at least for me) issues, like structure of language and communication, the nature of reality and consciousness, ethics of research, human evolution, causality, etc. are all present here, just don't expect a detailed yarn about each...just enough, I think, to get you to think.