Formulas for the Radial and Tangent Vectors in 4-space

  The minimum points, a, b, and c, are used to define the radial unit vector as follows.

   The tangent vectors generated by changes in the angles are found by taking the partial derivatives w.r.t. the spherical angles and converting the result to unit vectors.

  The set of four vectors forms an orthonormal basis which can be checked by calculating the dot products for pairs of the vectors in the basis B. Motion in any direction on the 4-sphere can be expressed by a linear combination of the tangent vectors.