Petra- “Treasury”
I started with the axes of the outer columns. I will call the distance from those axes to the centerline 1 unit, so that the width between those axes is 2 units. The height of the column shafts in the first story is 1 unit, so that this area forms a double square (slightly smaller than the one that you found around the exterior of the composition; more on that below…)
I stepped in by quadrature, and found the width of the door opening, which is (root2)/4, or .354, in addition to noticing that the right-hand column flanking the door sits further outboard than its pendant to the left.
I create a shaded orange square whose height matched that of the column shafts.
I circumscribe a circle around it, and I notice that the intermediate column axes are halfway between the sides of the square and the vertical tangents to the circle. The span between those orange vertical axes is therefore 1.207 = (1 + root2)/2.
The same circle reaches up to height 1.207, at the base of the figural frieze in the entablature.
I also create an arc whose center is the centerpoint of the façade baseline, so that it sweeps through the upper corners of the shaded square. The top of this arc locates the top edge of the capitals. This geometry relates to the Golden Section (Phi), such that the top edge of the capitals lies Phi-1 = 1.618 -1 = 1.118 units above the baseline. In other words, the height of capitals is 11.8% as great as the height of the shafts. The big double square that you discovered in your analysis, similarly, is 11.8% bigger than the one I got from the pier axes.
I also infer from this structure that the inner column axes are supposed to be .500 units apart, and that the greater displacement of the right-hand one is a mistake. I carry those orange axes upward to the top of the composition.
To climb upward, I first draw 45-degree lines from the corner of the shaded square, so that they converge at height 1.500. The slope of the main pediment seems to have been set by connecting the vertex of the resulting triangle with the points at height 1.207 on the outer column axes.
The principal horizontal crease just above the pediment is at height 1.618, i.e. exactly the Goldne section of the first story’s column height. This height can be found by unfolding the half-diagonal of the shaded square, and the heavy orange arc indicates. This will be a big deal for later.
Meanwhile, I also note that the orange diagonals launched from the column axes at height 1.000 converge at height 1.802, locating the top of the main blocks in the statue bases. These lines continue upwards to meet the column axes at height 2.618, or 1+Phi, which locates the base of the second, broken, pediment.
The top of the second story capitals falls at height 2.427, i.e. 3/2 Phi, as the three green semicircles along the left margin of the graphic indicate.
The base of the figured frieze seems to fall at height 2.496, which is Phi (1.118), found by unfolding the big green arc from the corner of the big double-square in first story, whose corner is the outboard corner of the capital.
The middle of the urn above the tholos appears to be at height 3.236, which is 2 Phi, so that the whole composition up to that level is a big Golden Rectangle, of which two subquadrants are shown gold-shaded in the graphic.
Although the photogram source image doesn’t clearly show the horizontal lip cut into the cliff above the main façade structure, it is tempting to imagine that it is 1.118 times larger, so that the whole composition would be an even larger Golden Rectangle precisely framing the outer corners of the façade structure.
Cool, eh?
This is the so-called Treasury from Petra, Jordan. The source image comes from Judith McKenzie, The Architecture of Petra. British Academy Monographs in Archaeology 1. Oxford: Oxford University Press, 1990, plate 80.