>
> I've searched a little bit more and I have not yet found a reference on
> the web. Mind you that is searching without knowing the author, any of
> the book titles or character names. Still I'd expect to turn up
> something based on the slim details that I do remember. Maybe this is
> the rare case where there is nothing to be found on a topic on the whole
> web?

I spoke too soon.

Here are the details found at http://www.larryniven.net/mega.shtml:

Author:  Colin Kapp
Title:   Cageworld 1:  Search for the Sun
          Cageworld 2:  The Lost Worlds of Cronus
          Cageworld 3:  The Tyrant of Hades
          Cageworld 4:  Star-Search

Type:    Dyson sphere (type II)
Description:

In the distant future, the Solar System has been transformed into a 
series of concentric shells (one for each planet, plus an extra one 
between Saturn and Uranus, if I remember rightly).  People live on the 
outer surface of each sphere, and have forgotten about the outside universe.

Dimensions of the system (overall):  diameter 12 billion kilometres; 
mass 5.2e36 kilograms (2.6 million Suns).

Which gives enough info to find more references:

http://en.wikipedia.org/wiki/Cageworld_series (very brief)
http://en.wikipedia.org/wiki/Colin_Kapp (not a lot of detail)
http://www.goodreads.com/series/50535 (this looks like the most detailed 
info on the books)

Yet another obscure interest from my childhood that can be revived 
through the wonders of the Internet.

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