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Circled helicoid
Torse column, coil, and SaintGilles screw (by Robert
March)
Other name: cyclic helicoid. 
Cartesian parametrization:
where is the parametrization of the circle a diameter of which lies on Ox, with center (a, 0, 0), radius b, forming an angle with the horizontal.
We get the SaintGilles screw for the torse column for and the coil for . 
The circled helicoids are the helicoids generated by the helicoidal movement of a circle.
Three remarkable positions of the generating circle can be distinguished:
Saint Gilles screw: vertical generating circle (in a plane containing the axis). 


The Saint Gilles screw in the case where the axis of the helicoid is a diameter of the circle ( and ) is called by [Gray] "corkscrew surface" or "twisted sphere"; its parametrization is: . 
See also "helihorns".
The original Saint Gilles screw, near Arles
Model made by Robert March 
The vault of this helicoidal staircase is half a SaintGilles screw. 
The torse columns (?) of the altar of St. Peter's Basilica in the Vatican 
Triple torse column 
The serpentine column at Istanbul; to what family does it belong???
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© Robert FERRÉOL 2017