In this interactive diagram we have the pentagram case of what we had
for pentagons in the previous diagram
and for triangles in the one before that.
It may be helpful to have seen those demonstrations first.
There are a red circle and inscribed regular pentagram
s, a blue circle and
inscribed regular anti-pentagram a
(with reversed orientation), red and blue radius
control points, green midpoints r
between corresponding red and blue
ones, and green lines making up the reentrant pentagram that results from
the construction. The radius controls and the points
s0 and
a0
are all draggable (as in the triangle case).

Initially the r points
are all in a straight line,
with a double point of r2
and r4 at the left,
r1 and
r3 in the middle, and the single
r0 at the right. Rotating
a0 a little bit splits the double points
and makes the situation easier to see.
The r points remain in a line
until the radii of the red and blue circles differ.
The resulting green figure is always an affine image of a regular
pentagram, or of its reverse (when the red radius is smaller than the blue).

Turning on [Tracing] by clicking it leaves a trail of yellow dots
marking where r0
has been as the mechanism is moved. Unfortunately, the only way to
turn tracing off is to refresh the page and restore the applet to its
start.