So I know in 3D there is Cartesian, Cylindrical, and spherical coordinates. So I am going to try to list and name 4D variants of these
Quickly listing of the 3D ones
Cartesian = (x , y , z)
-Clasic
Cylindrical = (cos(θ1)r1 , sin(θ1)r1 , z)
-Polar coordinates extruded
Spherical = (cos(θ1)sin(θ2)r1 , sin(θ1)sin(θ2)r1 , cos(θ2)r1)
-Polar coordinates revolved into a sphere
Now the 4D ones
Cartesian = (x , y , z , w)
-Clasic
Cubeinder = (cos(θ1)r1 , sin(θ1)r1 , z , w)
-Polar extruded 2 times
DuoCylindrical = (cos(θ1)r1 , sin(θ1)r1 , cos(θ2)r2 , sin(θ2)r2)
-Cartesian product of the polar coordinate system and the polar coordinate system
Spherinder = (cos(θ1)sin(θ2)r1 , sin(θ1)sin(θ2)r1 , cos(θ2)r1 , w)
-Spherical coordinates extruded
Hyperspherical = (cos(θ1)sin(θ2)sin(θ3)r1 , sin(θ1)sin(θ2)sin(θ3)r1 , cos(θ2)sin(θ3)r1 , cos(θ3)r1)
-Spherical coordinates revolved into a hypersphere
Is there any I missed? Is there any interesting ones beyond 4D?