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?