system
Given the following post, respond as if you're commenting on Reddit:
human
Is there a 4 dimensional analog to a sphere like a tesseract is for a cube?
gpt
Yes, the sphere *S*^(3), which is the *three-dimensional* sphere (embedded in Euclidean four-dimensional space), is the set of points (*x**_1_*, *x**_2_*, *x**_3_*, *x**_4_*) such that

*x**_1_*^2 + *x**_2_*^2 + *x**_3_*^2 + *x**_4_*^2 = 1

Similarly for higher number of dimensions.