-rotation
now only 
-rotation is taken to be the
identity transformation in the geometrical space. With respect to
a given P-orientation of an initial unextended manyfold, vector
or pseudovector one, there may be constructed two different
spatial spinors, 
and 
, respectively. By definition,
those spinors provide us with points of the extended space
models, each spinor is in the correspondence
with points of a vector space. For both models an explicit
parametrization of the spinors
and by spherical
and parabolic coordinates is given, the parabolic system turns out
to be the most convenient for simple defining spacial spinors.
Fours of real-valued coordinates by Kustaanheimo-Stiefel, Ua
and Va, real and imaginary parts of complex spinors
and respectively, obey two quadratic constraints. So that
in both cases, there exists a Hopf's mapping from the part of
3-sphere S3 into the entire 2-sphere S2. Relation
between two spacial spinor is found: 
, in terms of Kustaanheimo-Stiefel
variables Ua and Va it is a linear transformation from
SO(4.R), which does not enter its sub-group generated by
SU(2)-rotation over spinors.
Key words: Cartan, spinor structure, P-orientation
