Sacred Geometry
In Christianity, the mandorla symbolizes the light that surrounds Christ. In medieval, Romanesque, and Byzantine art, it was used to show Christ in majesty — Christ seated on the throne of the world. In the Eastern Orthodox Church, it is also used in Resurrection and Transfiguration icons. The mandorla is the almond-shape figure at the center of the vesica piscis, a construction in which two circles overlap. (Mandorla means "almond" in Italian.)
Christ in Majesty, Codex Bruchsal 1 01v, c. 1220, Badische Landesbibliothek, Karlsruhe, Germany.
This is a true vesica picsis construction — the center of each circle falls on the perimeter of the other.
The artist who painted the altar frontal, below, began with a standard rabatment of two squares and then placed a mandorla-type figure in the area of overlap. Unlike the Christ in Majesty illumination, above, the circles are too close together be a true vesica piscis (their centers are not on their perimeters).
Christ Blessing, 1120-50, tempera on wood, 97 x 123 cm, altar frontal from the Romanesque church of Sant Marti de Puigbo, Gombren (Ripolles), Catalonia.
The armature of Rogier van der Weyden's Descent from the Cross, below, appears to be a mandorla derived from a true vesica piscis. A mandorla fits the painting's format exactly. In addition, the center points of circles that could have been used to establish the height of rectangular extension at the top are located on the mandorla. Note that the body of the dead Christ follows the curving line made one of these circles. Can it be a coincidence, then, that the other figures are positioned and posed to lead the viewer on an mandorla-like path around the painting?
Rogier van der Weyden, The Descent from the Cross, before 1443, oil on panel, 205 x 262 cm, Prado.
In my opinion, this is one of the most beautifully and elegantly designed paintings in the history of art.
Van der Weyden was one of the Northern Renaissance artists who appears to have designed his religious paintings on foundations of sacred geometry. In The Seven Sacraments triptych, below, the golden rectangle has replaced the overlapping squares seen in southern Proto-Renaissance altarpieces.
Rogier van der Weyden, The Seven Sacraments, 1440-45, oil on panel, 223 x 200 cm, Royal Museum of Fine Arts Antwerp.
The central panel's format is a vertical golden rectangle topped by a horizontal golden rectangle in which half of an ellipse has been inscribed. The location of the altar suggests that van der Weyden wanted a golden spiral to coil into infinity at the apex of its alcove, above the head of the Madonna statue. The side panels' format is also a golden rectangle, with arches above them. The height of the arches seems to have been determined by intersecting circles with a radius of two-thirds the width of the format.
Van der Weyden was a contemporary of Jan van Eyck, and both may have been taught by Robert Campin. As I suggested in the Rabatment section, van Eyck may have brought rabatment to the north.8 However, after The Adoration of the Lamb, he seems to have developed his own armature style — they are complex and absolutely saturated with sacred geometry. They are difficult to decipher because he appears to have had a penchant for free-standing geometric figures — constructions that are suggested by the painting but that are not necessarily integrated into the armature. Consider his Madonna at the Fountain, below.
Jan van Eyck, Madonna at the Fountain, 1439, oil on panel, 19 x 12.5 cm, Koninklijk Museum voor Schone Kunst, Antwerp.
The format consists of two horizontal golden rectangles above a row of three squares. Right above the squares is the brick planter. The band that contains it consists of three horizontal golden rectangles. Since golden rectangles have the unique characteristic of being infinitely divisible into a square and another golden rectangle, it can also be said that there are three vertical golden rectangles at the bottom of the format. The portion of the tapestry behind Mary that is above the planter is also a golden rectangle. This one is a little off-center and not part of the format armature. Was it intentional? Probably, but there's no way to corroborate it.
Jan van Eyck, The Lucca Madonna, c. 1437, oil on oak, 66 x 50 cm, Stadel Museum, Frankfurt.
The armature of the Lucca Madonna, above, appears to be a set of sacred geometric figures that relate to the image, to one another, and to the height of the format. The width of the format seems to have been ignored. If the sides of the tapestry behind Mary are extended to the top and bottom of the format and bisected horizontally, two vertical golden rectangles result. The chair canopy's slope is sixty degrees — just like an equilateral triangle's. An equilateral triangle drawn at the bottom of the format with a base the width the rug will meet the canopy triangle at its lowest point. This, not coincidentally, is the picture's vanishing point. Was van Eyck drawing triangles or orthogonal lines? Possibly both: If a golden triangle with a base the width of the rug is drawn, its apex occurs at the top of the format. If a square with sides equal to the width of the top equilateral triangle is drawn at the top of the format, it ends at the vanishing point. Moreover, these spatial divisions are supported by the image. Mary's red robe forms a triangle that is reminiscent of the golden triangle. She and the baby Jesus are beautifully framed in the section of this triangle that's inside the upper golden rectangle — which is itself a golden triangle.
Van Eyck, I think, was not particularly interested in being constrained by the proportions of the format. I haven't found a standard primary rabatment in any of his paintings other than The Adoration of the Lamb. His fascination with sacred geometry was taken up by younger artists, including Petrus Christus and Hans Memling. Here are examples of their armatures:
Petrus Christus, Nativity, 1452, oil on panel, Groeninge Museum, Bruges.
Hans Memling, The Last Judgment triptych, 1467-71, oil on panel, 241 x 181 cm (center panel). National Museum, Gdansk, Poland.
The internal divisions of the Petrus Christus armature are supported by the top and bottom of the format and by the picture itself. The green triangle is an equilateral triangle. In the central panel of the Hans Memling armature, there are two primary rectangular divisions that represent the domains of heaven and earth. The heaven rectangle is comprised of two vertical golden rectangles. A golden rectangle is infinitely divisible into a square and a golden rectangle, and Memling has divided and subdivided these golden rectangles a number of times. Then he has used points along the format's midline where the lines intersect to draw two circles and an ellipse. The ellipse centered in the earth rectangle is suggested by the arrangement of the figures emerging from their graves and being weighed.
In southern Europe, sacred art armatures were more restrained and formulaic. Golden rectangles were used only occasionally, and much more judiciously.
Raphael, Ansidei Madonna, 1505, oil on poplar, 217 x 148 cm, National Gallery, London.
Raphael's format is a square with a half-circle above it. The width and placement of the throne indicates that the square was divided vertically into thirds. A golden rectangle placed above the middle section separates the throne from its canopy and shows that the format square was also trisected horizontally — the upper middle square together with the golden rectangle comprise a larger golden rectangle. Orthogonal lines have been used to create the illusion of depth, but in terms of the armature, they are essentially irrelevant. (The two orthogonals at the bottom are not the sides of an equilateral triangle.)

8 I haven't looked at the armatures of medieval partings from this region, so I don't know the extent to which van Eyck affected the design of sacred art in the north.