Although this was a rather less common method for constructing eight salient stars used as the outlines for field fortifications, it does make an occasional appearance in old maps and plans of field works. This construction also begins with the construction of a square, but goes on to reduce all eight salients to 60 degrees, leaving alternating salients (those that began life as the corners of the original square) in a somewhat retired position between more advanced salients constructed from the sides of the original square.

Construct a square. Mark the corner angles as A, B, C, and D.

Trisect each side of the square. This must be done by measuring the length of the sides and dividing that length into three equal segments.

Construct equilateral triangles on the center segment of each trisected side.

Produce two diagonals through the center of the square (AC and BD). Extend the salient legs of each equilateral triangle to the diagonals inside the square. Mark the points where the lines of the faces intersect the diagonals (K and N in the illustration to the left, L and M in the next illustration).

Repeat the foregoing operation for each side of the square. Note that collateral faces will intersect on the diagonals that fall between them: Face EK intersects Face FK on Diagonal AC.

Construct the faces of the retired salients by producing lines from each corner of the square to the point where faces intersect on the next diagonal (diagonals have been erased here to clarify the source and end point of the lines used to form the faces of retired salients). In this case a line has been produced from Point A (a corner of the square) to Point L, the point where Faces FL and GL intersect.

To further clarify things, the second face of the retired salient has been produced from Point A to the point of intersection on the next diagonal at Point N.

Repeat these operations to construct the lines of the faces of the retired salients, one corner of the square at a time.

Once all the lines for the faces have been drawn it will be necessary to start erasing those parts of the lines that are not actually part of the outline of the eight salients. This must be performed with some care; this construction produces a tangle of intersecting lines and it is a little too easy to obliterate the wrong part of the wrong line.

Erase those parts of the lines used to position of the faces of the retired salients that fall inside the point where the they intersect the face lines of the advanced salients.

Starting from point A parts of face lines AL and AN) have been erased as have parts of face lines EK and FK.

After carefully erasing all the extraneous face lines, leaving only those parts of the lines that actually form the outline, the eight salient star will be left superimposed over the original square. Erase the square.

Once the square has been rubbed out a really nicely shaped eight salient star with 60 degree salients remains.

~ An Instructive Animation Wherein the Foregoing Construction is Visually Explained ~