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CONOCUNEUS

Surface studied by Wallis.
Used in architecture to make a certain type of vault ("back arch of Saint-Antoine", "groin vault"...)
From the Latin conus "cone", and cuneus "corner").
Other name: conical wedge.

 
Cartesian equation of the conocuneus with axis Oz, directrix plane z = 0, and directrix the circle .
Quartic surface.
Cartesian parametrization: , with k = b /a.
Cylindrical equation in the case a = b.

Intersection with the plane x = h, ellipse with semi-axes b and kh=c.
Volume of the trunk of conoid delimited by this plane and the axis Oz.
 

The conocuneus is the right conoid with directrix a circle parallel to the axis.
 
Casts shaped like half conocunei, made by Alexandre Demir.

 

Recognize the conocunei among these familiar objects...
 
 


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© Robert FERRÉOL 2017