  We show that the pure entangled three-qubit symmetric states which are
inequivalent under stochastic local operations and classcial communication
(SLOCC) exhibit distinct geometric representation in terms of a spheroid
inscribed within the Bloch sphere. We provide detailed analysis of the SLOCC
canonical forms of the reduced two-qubit states extracted from entangled
three-qubit pure symmetric states. Based on the Lorentz canonical forms of
these states we arrive at two different geometrical representations: (i) a
prolate spheroid centered at the origin of the Bloch sphere -- with longest
semiaxis along the z-direction (symmetry axis of the spheroid) equal to 1 -- in
the case of pure permutation symmetric three-qubit states constructed from 3
distinct spinors and (ii) a spheroid centered at (0,0,1/2) inside the Bloch
sphere, with fixed semiaxes lengths (1/sqrt{2}, 1/sqrt{2}, 1/2) when the
three-qubit pure state is constructed via symmetrization of 2 distinct spinors.
