Calculating an antipodal point on a sphere Consider a 3-sphere at the origin $(0,0,0)$. Let $s_1 = (x,y,z)$ be a point somewhere on the surface of the sphere. How do I calculate the antipodal point $s

Calculating an antipodal point on a sphere Consider a 3-sphere at the origin $(0,0,0)$. Let $s_1 = (x,y,z)$ be a point somewhere on the surface of the sphere. How do I calculate the antipodal point $s_1^* = (x^,y^,z^*)$?

For a sphere centered at the origin, the antipodal point is the one you obtain by negating all coordinates: $s_1*=(-x,-y,-z)$.

Note that “3-sphere” usually refers to an object in fourdimensional space. So I think you mean 2-sphere. See also $n$-sphere at Wikipedia.

Calculating an antipodal point on a sphere Consider a 3-sphere at the origin $(0,0,0)$. Let $s_1 = (x,y,z)$ be a point somewhere on the surface of the sphere. How do I calculate the antipodal point $s_1^* = (x^*,y^*,z^*)$?

Calculating an antipodal point on a sphere Consider a 3-sphere at the origin $(0,0,0)$. Let $s_1 = (x,y,z)$ be a point somewhere on the surface of the sphere. How do I calculate the antipodal point $s_1^* = (x^,y^,z^*)$?