Unlike the constructions used to create four and five salient stars, a six salient star does not need to begin with the construction of a regular polygon with the same number of sides as the star has salients, that is, in this case, a hexagon. It is rather quicker to begin by constructing an equilateral triangle of the appropriate perimeter and using its three sides to produce the requisite number of salients.

Given a right line AB that is 9 inches long begin constructing a six salient star by first constructing a equilateral triangle.

Using Point A as center describe an arc of a circle that has a radius equal to the length of Line AB (9 inches).

Describe a second arc with a radius equal to the length of Line AB centered on Point B. Mark the point where this arc intersect the first arc as Point C.

Produce right lines to connect consecutive points: A to C, C to B. These lines form the three sides of an equilateral triangle.

Trisections can only be performed by measuring the sides (9 inches in this case) and dividing the length by three (9/3=3). Once the third part is known the sides can be trisected by opening the compass to the appropriate scale length (3 inches) and using each angle as a center to describe arcs that cut adjacent sides of the triangle.

Complete the six salient star by constructing equilateral triangles on the center segment of each trisected side.

Each face of the six salient star is 1/12 the perimeter of the star. In this example each face is 3 inches long giving the star a perimeter of 36 inches. Each side of the original equilateral triangle is 1/3 of the constructed star's perimeter, a proportion that is very useful to know when the perimeter of the star is given and the exact measure of the sides of the equilateral triangle must be determined.

Finally, remove all construction lines and marks to make the six salient star look neat and clean.

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