page_title: Hexafoil
section_title: Creating a hexafoil
hierarchical_section_title: Hexafoil / Creating a hexafoil
caption_attribution_description: Italiano: Vetrata interna di Notre-Dame a Parigi
context_page_description: A hexafoil is a geometric design that is used as a traditional element of Gothic architecture, created by overlapping six circular arcs to form a flower-like image. The hexafoil design is modeled after the six petal lily, for its symbolism of purity and relation to the Trinity. The hexafoil form is created from a series of compound units, and exists as a more complex variation of the same extruded figure. Other forms similar to the hexafoil include the trefoil, quatrefoil, and cinquefoil.
context_section_description: One common form of the hexafoil has a ring of six tangent circles circumscribed by a larger circle. It may be constructed by compass and straightedge, by drawing six circles at the centers of a regular hexagon, with diameter equal to the side of the hexagon. The inner circles of the hexafoil have radius 1/3 that of the outer circle containing them, from which it is possible to derive the area and perimeter of the figure as a mathematical exercise.
  Another method of drawing a hexafoil is the vesica piscis method.  To do so one takes a ruler and uses it to draw a line.  A compass is used to draw a circle.  The needle point is put on the point where the perimeter of the circle intersects the horizontal and the drawing point on the center of the circle to draw a curved line that intersects two points of the perimeter of the circle.  This makes the vesica piscis shape.  The needle point of the compass is then put on the points where the vesica piscis intersects the perimeter of the circle and another semi circle is drawn, terminating at the perimeter.  One then continues drawing the semi-circles at the points where they intersect with the circle's perimeter until all points are connected and the shape is a hexafoil.
caption: Hexafoil in stained glass window at Notre Dame
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