This is an interesting problem in that you have many interrelated dimensions and constraints. I first tried to determine the dimensions of the diamond and corresponding offsets with AutoCAD's parametric solver but that got a bit messy so I went to an algebraic solution aided by Excel/s Goal Seek solver.
If we assume basic dimension for the diamond as follows:
and since we know that the overall dimensions are 403 x 1195 the following expression can be stated from the width:
3 * a - 2 * c =403 [1]
and from the height
6 * b - 5 * d = 1195 [2]
Re-arranging [1] and [2] we have
a = (403 + 2 * c)/3 [3]
b= (1195 + 5 * d)/6 [4]
Since a/b = c/d, and using equation [3] and [4] we can write that:
c/d = ((403 + 2*c)/3)/ ((1195 + 5*d)/6) [5]
rearranging we have:
6*d*(403/3 - c/6) - 1195 * c = 0 [6]
The challenge here is to determine values for c and d (other than 0) that will yield 0 for the left side.
We also know that the offset line for c and d is related to the thickness t of the lead strips and that t = 12.
From similar triangles we have:
t / c = b / (a^2 + b^2)^0.5 [7]
solving for t yields:
t = (b * c) /((a^2 + b^2)^0.5) [8]
I set up an Excel spreadsheet as seen below. Cells E1, E2, E3 contain equations [3], [4], [8] repsectively.
Cell B5 contains equation [6]. I make an initial guess of c= 10, d = 20 and note that b5 = 3970. It should equal zero. Using Goal Seek as follows:
yields the following:
Note that B5 is 0 but t = 11.05599. We want this to be 12.
By changing guesses for d and computing the corresponding value for c with Goal Seek we find that d = 21.8 and c = 14.44 yields a value of t = 12.038 which may be close enough to 12. If not we can tweak the value for c and recalculate.
We now have all the dimensions we need to draw that pattern.
Edited a couple of typos 9/23/2022.
lee.minardi
