  Stereo mini-jet cells will be indispensable components of a future $e^+e^-$
linear collider central tracker such as JLC-CDC. There is, however, no official
Geant4 solid available at present to describe such geometrical objects, which
had been a major obstacle for us to develop a full Geant4-based simulator with
stereo cells built in. We have thus extended Geant4 to include a new solid
({\tt TwistedTubs}), which consists of three kinds of surfaces: two end planes,
inner and outer hyperboloidal surfaces, and two so-called twisted surfaces that
make slant and twisted $\phi$-boundaries. Design philosophy and its realization
in the Geant4 framework are described together with algorithmic details. We
have implemented stereo cells with the new solid, and tested them using
geantinos and Pythia events ($e^{+}e^{-}\to ZH$ at $\sqrt{s} = 350 {\rm GeV}$).
The performance was found reasonable: the stereo cells consumed only 25% more
CPU time than ordinary axial cells.
