Index | Article: "Scenes from a Design:The Plan of Saint-Urbain, Troyes" | page 2, page 3, page 4, page 5

Page 4

The Four Octagons
Figure 7

The series of rotating squares and golden section rectangles establish the proportions of the major spatial blocks and fix the locations of the mural envelope and interior supports. The second square in the sequence closely approximates the alignment of the polygonal walls of the apse and flanking lateral chapels (fig.2). The 'apse itself is designed around five sides of an octagon.
To find the geometric center of the apse. an arc whose radius is one-half the diagonal of the sixth square (4.63 meters) is swung eastward from the center to intersect with the centerline of the plan (fig.8). The octagon which defines the inner wall surface of the apse could be generated from a circle whose radius is 5.29 meters. that is. one-half of a side of the crossing square: the diagonal of the octagon. 10-58 meters, equals a side of the crossing. A subtle. but tangible geometrical connection is thus created between the center of the building and its liturgical sanctuary.

Remarkably, an identical geometry underlies the disposition of the- transept, porches and the central portal of the west facade (fig.7). Transferred to the exterior of the transept, aligned with the north-south axis of the plan and the line of square one (AE or BH), the sides of the 'apse' octagon mark the inside faces of the buttress salients of the porch and its center locates the apex of the trumeau between the two doors. The placement of the slim free-standing porch columns is found by inscribing a square within the octagon. In the central portal of the west facade, the octagon, laid on the western line of the site (EH) and aligned with the east-west axis, appears to dictate the length of the west bay of the nave while its side fixes the interval between the free-standing porch columns.

Saint-Urbain's west, north, and south porches, as revealed by the geometry, are neither additive nor independent features of the plan. 'Me placement of the octagons pulls the polygonal and projecting spaces on the cardinal axes in toward the interior; conversely, the apse and porches become coherent extensions of spaces which unfold outward like the petals of a flower. Geometrically tied to the crossing about which they orbit. the four octagons superimpose a cruciform figure on the basilican plan. The insistent centrality identifies Saint-Urbain not only as a shrine, a memoria to martyr saint and papal patron, but likely represents it as a shrine to the Corpus Christi. Devotion to the body of Jesus was a matter of intense personal interest to Urban IV who promulgated the new feast of Corpus Christi in 1264 and the sacrifice of Christ forms the central theme of the stained glass program of the apse.

Chapels and Portals
Figures 8-9

Like the main apse. the five-sided chapels which form the eastern termination of the aisles are based on a regular octagon (fig.8). Further. the circle that circumscribes the octagon bears the same geometrical relationship to the aisle as the apse to the central vessel: its radius (3.27 meters) is half the width of the aisle and the diagonal of the octagon (6.54 meters) equals the aisle width. The center can be found through a purely mechanical process by stretching the radius to the east-west axis line of the aisle from the intersection of line FG and south edge of block b2 (figs.4,8)

The Saint-Urbain designer conceived the three portals of the west facade as exterior reflections (or anticipations) of the interior (fig.9). Again, geometry provided the connections as it also served as the vehicle for variety. As we have seen, square 5 in the rotational sequence and the side of the octagon set the width of the central portal and the spacing of its columns respectively. The ratio of the depth of the entry (2.48 meters) to the side of the octagon (4.05 meters) closely approximates a golden section.

The geometry of the deep lateral portals is considerably more complex, less transparent (fig.9). I have built the following solution on the assumption that the Saint-Urbain master, as he did throughout the design, locked these entries into the plan as a whole through the repetition of or geometric variation on other polygons and dimensions. First, the octagon of the lateral chapels is laid on the western line of the site (EH), the five sides determining the depth of the portal and wall. Second, a perpendicular line (de) equal to the side of the apse/ central portal octagon (4.05 meters) is constructed from the midpoint of the east side of the octagon. This line's end point (.225 meters east of ER) not only serves as the center for the construction of a series of geometric forms that compose the portal but also marks the flat face of the facade salients. A square locates the inside surface of the lateral walls and the exterior plane of the doorway wall. At 5.70 meters per side, it was surely derived from square 5 (the central portal width) through the construction of a golden section (fg). Thus, the dimensions of the central and lateral portal openings maintain the relationship of the nave and aisle spaces. The distance between the side of the crossing square (10.58 meters) and square 5 (9.25 meters) yields the thickness of the west facade salients. Finally, from the same center a hexagon is laid out to position the angled walls of the portal. Anchored to the axes of the flanking buttress salients, the hexagon can be inscribed in a circle with a radius of 3.50 meters. By using the hexagon, the Saint-Urbain designer at once created polygonal entries that echoed the chapels to the east, yet achieved a subtle independence. This same love of rich formal diversity within a tightly woven framework will characterize his tracery compositions.