Abstract
In this note we shall determine which Mimura-type spherical 2-designs are rigid. Furthermore we show that spherical 2-designs of d + 2 points in Sd-1 are rigid by showing the spherical 2-design of d + 2 points is unique. We also establish that a 2-design of d + 3 points is non-rigid. This work is intended to shed some lights on conjectures of Bannai. Bannai conjectured [Ba2] that there exists a function f(d, t) such that if X is a spherical t-design in Sd-1 and |X| > f(d, t), than X is non-rigid. He has showed that f(2, t) = 2t + 1.
