Miraculously, the original Head-Hand-Foot circles - which I had first fitted to the image by eye, and without consideration for any plan other than form itself - fall into the kind of position with the Monkey Star (the X-Star 3), which is easily and completely described in general geometrical terms. This means that we can reproduce the circles to scale in the position of any given 5-pointed star.


This reconstruction above involves a number of alignments either parallel, or perpendicular to the Big X's line 'b on the left above.

Hand-circle's Exact Coordinates
The monkey's hands invoke the inner X-Star circle with admirable accuracy.

First coordinate for the Hand Circle:

The Hand-circle centers right on (+/- 3mm) the vertical line b1 emanating from the star's tip just above. Hence line b1 is a major line in the Monkey Star's grid.

Second coordinate for the Hand Circle.

Pentagon No. 2 in the diagram above is a direct projection of the inner pentagon of the Monkey Star. When it rotates about the Monkey Star's center, its tip describes a circle (in yellow above), which is tangent to the Hand-circle (see below). This solves the second coordinate for the Hand-circle.


At this point, we can reconstruct the Hand-circle, and the line-1, which is the laser-like line of sight from the center of the Monkey Star through a pointlike aperture between the hands. We can also reconstruct line 3.

Foot-circle's Exact Coordinates
First coordinate of the Foot Circle:

When we inscribe a pentagon into the Foot-Circle, its vertical side (b5) passes through the center of the Monkey-Star (X-Star 3). In the diagram above, the vertical side of the (purple) pentagon No.2 originates from the center of the X-Star. It shares all its verticals with the Foot-Circle's pentagon, as if the Foot Circle's pentagon was its projection directly downwards. With 'b' vertical, it is as if the monkey were standing up.

Second coordinate of the Foot-circle:

This idea is straightforward. The Line-3 originates at the same point, at which the Line-1 exits the Hand-circle. It is vertical to 'b', and also a tangent to the top of the Foot-circle. This line gives the Foot-circle's elevation. Now, we may reconstruct the Foot circle, as well.

Special Effect

Two distances involved measure 17.9999.. X-Star meters - almost a perfectly round value: These are the distances of the centers of both the Foot-circle and the Monkey Star to the nearest corner of the other circle's pentagon.

The Head-circle
First coordinate of the Head Circle

A line through the Head Circle's center perpendicular to the line-1 is a tangent to the inner X-Star circle. And the line drawn from the center of the X-Star as a tangent to the Head Circle will be perpendicular to the line-1. This yields one coordinate.

The second coordinate for the Head-circle

It is given by the Main Square, not seen in the diagram above. It involves a major line of the square's grid through the 1/4 point of its diagonal 'y'.

The distance between the centers of the Head-circle and the Cone's Key-circle is quite interesting
 

11.777,777,67...   X-Star meters.

Truly, the monkey performs so many fine balances and alignments, a most adroit android could not easily duplicate them all! I wonder, could an android, or a robot make good use of a long tail?

A smiley is mandatory here, but the question is as good as any.