The fine structure constant from the separation distance of two 3-branes in the covering space of a toroidal orbifold

4-branes that wrap the long and short fundamental 1-cycles of a rectangular toroidal orbifold T 2 /(Z2) 3 , which has Planck-scale compactification radii, intersect after 43 and 109 wrappings, respectively, in a 3-brane upon which the scale factor, equal to a power of the inverse of compactification length, has precisely the same value when measured parallel to either of the fundamental 1-cycles. The scale, 5.12 MeV, of the 3-brane is reduced from Planck scale by a factor 137 -10 . The distance of the 5.12 MeV intersection from the Planck brane in the orbifold covering space is precisely equal to the length of 40 cycles of the orbifold diagonal, and measures 137 Planck units. A geometric ‘Sequence of Scales’ extends from 5.12 MeV to both larger and smaller scales, and is associated with the intersections of two 4-branes, with wrapping numbers (1, 2) and (1, -2). All fields may be confined to 3-branes. Weak, strong and electromagnetic 3-branes are identified; all three are associated with ~integer wrappings of the orbifold diagonal. The electromagnetic 3-brane is located adjacent to the 5.12 MeV 3-brane, at a distance of 137.0359 Planck units from the Planck brane in the orbifold covering space. The scale on the electromagnetic 3-brane, 4.927 MeV, is related to the scale on the weak 3-brane, 91.1876 GeV, by a factor 137 -2 .