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SINUSOIDAL CONE
n = 1 
n = 2 
n = 3 
n = 4 
n =1/2 

Cylindrical equation:
(surface with rotation
symmetry).
Cartesian parametrization: (). Algebraic surface when n is rational. 
The section by a cylinder with axis Oz is the reunion of two sine wave cylinders (symmetric images of one another about O).
The section by a sphere centered on O is the reunion
of two cylindric
sine waves (symmetric images of one another about O).
The section by a horizontal plane z = b is an
epispiral:
.
Compare to Plücker's
conoid.
We can also consider the secantoidal cone, with cylindrical equation , i.e. , for which the section by a horizontal plane is a rose: . 
Pencil shaving, by Levi Capareda
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© Robert FERRÉOL 2017