Desargues's Golden Configuration (female)

If you are reading this, then it's likely that you already know about Desargues's Configuration.  If you don't, then you should look it up somewhere.  It's an important, classical construction from projective geometry.

In this realization, the points are represented by spherical balls and the lines are represented by bars.  With a faithful realization, you should be able to see 3 balls on every bar and 3 bars intersecting at every ball.  If you count, however, you should notice that there are only 9 balls.  Also, there are 3 segments with only 2 balls apiece.  These segments must intersect, according to the theorem of Desargues.  As it turns out, for this realization, these three segments are mutually parallel.  Thus, they indeed meet at an imagined 10th point at infinity.

But, there's more.  The three mutually parallel segments are in Golden Proportion.  That is, the three segments are in the proportion (1/t:1:t), where t=(1+sqrt(5))/2 is the Golden Ratio.  In fact, more is true: Among all of the segments with 3 finite points, the intermediate point divides the segment according to the Golden Section.  The Golden Ratio is everywhere in this model, so this is why we might call it "Desargues's Golden Configuration".