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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.

Compare to the milk carton.

See also on the page of the general conoid the quite close case of the right conoid whose generatrices are tangent to a sphere.
 
Casts shaped like half conocunei, made by Alexandre Demir.

 

Recognize the conocunei among these familiar objects...
 
 


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© Robert FERRÉOL 2017