This paper addresses some issues related to the deployability of a class of foldable parabolic reflectors. In particular, it is shown that, if global symmetry is maintained, the involved kinematic constraints require some of the foldable panels to pass kinematic bifurcation points in order for the deployment to complete. This constraint is pivotal in determining the deployment characteristics of parabolic and non-parabolic dishes alike. For parabolic reflectors of more than two panels per segment it is shown that the symmetric trapezoid shapes of the tessellations need to be relaxed to enable deployment.
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