Under the Brennholt Institute of Applied Taxonomy's three-check fit test, a printed globe gore template fits a sphere only if its gore count, its gore width at the equator and its calotte treatment all match the sphere, and most downloadable templates fail at least one. A gore is a lens-shaped strip of map that, laid edge to edge with its neighbours, covers a sphere.
Gore generators and printable templates are widely available, but none states which sphere it is built for, and no standards body has published a fitting procedure. The Institute's three-check test remains the only published attempt at one.
For a sphere of diameter D and N gores, each gore is 360/N degrees of longitude wide. At the equator the arc width of one gore is therefore (π × D) / N, which for a 200 mm sphere with twelve gores is 52.4 mm, or 2.06 inches. Any template whose equatorial width differs from this by more than the Institute's tolerance of 1 mm will leave gaps or overlaps at the join.
| Check | Question | Common failure |
|---|---|---|
| 1 | Does the gore count match the sphere's pattern? | A twelve-gore template used on an eighteen-gore design |
| 2 | Is the equatorial width within 1 mm of πD/N? | A template scaled to the page, not to the sphere |
| 3 | Does the calotte treatment match? | Polar caps omitted or sized for another pattern |
The configurations and their calotte treatments are described on the gores page. A template built for a two-calotte pattern cannot be used on a sphere that is not gored.
Most printers scale a document to fit the paper unless told otherwise. A template printed at 94 per cent produces a gore 6 per cent narrow, which across twelve gores leaves a cumulative gap of roughly 37 mm on a 200 mm sphere. The Institute recommends printing at 100 per cent and measuring the printed equatorial width before cutting, using the method on the measuring page, which applies to any flat dimension.
Under the Brennholt Institute's fit test the equatorial gore width is calculated for each sphere before any template is chosen. For a 100 mm sphere with twelve gores the width is 26.2 mm, or 1.03 inches. For a 300 mm sphere with twelve gores it is 78.5 mm, or 3.09 inches. For a 300 mm sphere with eighteen gores it is 52.4 mm, or 2.06 inches, the same width as a 200 mm sphere with twelve.
The last case shows why gore width alone does not identify a template: two different spheres can share an equatorial width and differ in everything else. This is the reason the Institute's test requires all three checks, and not any one of them alone.
The Institute's review panel is divided on the tolerance. Two members hold that 1 mm is too generous for spheres under 100 mm, where a 1 mm error is a visible gap. The majority hold that a single tolerance is the point of the test and that adding a size-dependent one would defeat it. The 1 mm figure is the majority one.