Folding Grids

[Jonnycakes]

With this months' folding challenge (anything from a triangle), I find myself needing to fold a grid over an equilateral triangle. A hex-grid would not normally be a problem, but I am having trouble getting an accurate one from a triangle. Do any tessellators (or anyone) out there have any tips? (I need 54ths, by the way)

[origamimasterjared]

I ain't no dirty tessellator, but I can tell you a trick or two using a little geometry.

The center of an equilateral triangle is 2/3 of the way between the point and the opposite side.

Use this three times and you've got your 27ths.