The Geometry of Quatrefoils

 

 

Yes! What a quatrefoil! 

What amazing craftsmanship! What exuberant geometry! The interrelated series of curves are such fun to study. 

The fretwork is part of an Episcopal church in Cody, Wyoming,

The photograph, by Travis Wade, Cabinetmaker, is shared here with his  permission. His shop, the  Atlas Cabinet Shop. LLC , is repairing/reconstructing the fretwork. (It is not nearly as pink as this image.)   

I, of course, was especially interested in the  geometric shape -the quatrefoil - at the center of this fretwork, the basis of the design. 

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Here, because the layers of  'tendrils' are an important part of the design, the layout of the circles with space for 2 rows of tendrils had to be the first concern. (A). Would it fit? How?
Then the size and profiles of the tendrils. 

Lastly: the size and shape  of the quatrefoil: should the foils be circular, oval,or ellipse? (B)

 

 Here is a  simple quatrefoil:  a shape: 4 lobes on the ends of crossed lines. The word in French means '4 leaves'.  

 

 

 

 

This form is one variation, the lobes are 1/4 the width of the cross.  

 

 

 

 

Or: the lobe is a half circle which if completed would be a circle.The design is 2 circles in width and 2 in height. 

 

 

This 13th C. stained glass window in Chartres Cathedral is a quatrefoil with another inside it. The inner quatrefoil overlaps the outer lobes.    

There are about 40 quatrefoil windows in Chartres, some small spots of light and color, others part of the larger windows. These quatrefoils surround the story of Adam and Eve.*   

 

 

 

 

 

 

Here is another quatrefoil. Its layout is more complex.

 

 

 

 

It's used here in the fence at the Abbey of Saint-Denis, Paris, France.** 

  

 The Abbey has been there since the 5th C. CE,  but the structure we see today was mainly built in the 12th and 13th C., It's been rebuilt regularly since then.

I have no date for the fence. Maybe Second French Empire 1852-1870?  

 

I imagine the ironmonger measuring the length of the fence, dividing it into segments; then laying out his grill sections in each segment.  

He knows what he wants to create.

The square is the base for his geometry. The welding points on the fence  connections are at the centers of the sides of each square. All his pieces  - the leaves of his quatrefoil - will be the same.  He will attach each one at the center of the rails, and to each other at the arrows. 

 

 

 

 

He needs to lay out the shape of the arcs. Using the rule of thirds he divides his sections into 9 squares, 3 across and 3 tall.

The diagonal of the square is the diameter for the  circle he will use for his lobes. The lobes are bigger than the squares and would overlap. (See the next diagram.) So they are slid toward the center. 

 

 

Finally he  joins each square to its neighbor where they intersect and adds an arrow over the weld.

The design of this quatrefoil is much more complex than the first one. But visually it is much less intense. It is just a fence using 13C. visual language.  

 

The layouts comes with a caveat: The images from Chartres Cathedral, the Abbey of Saint-Denis and the church in Wyoming are all photographs.They were taken at an angle. I cannot check my geometry with  dimensions.  

Wikipedia has an excellent review of the shape's  religious connotations in many cultures.  But good images and  measured drawings of quatrefoils have been  difficult to find. 

*Chartre Cathedral, France, from the book Chartres Cathedral, text by Malcolm Miller, photographs by Sonia Halliday and Laura Lushington,  Riverside Book Co., NYC. 1996

**This image comes comes from the Buffalo, NY, Historical Museum website. The photographer is  Chuck La Chiusa.