The variables that can be independent are in capitals.

For smooth operation start with the default values.

The formulas used here are derived from well known trigonometric identities at proof_new.txt They are rendered in MathML at exact_tbl.xml . Further derivations are at plato.txt and they are rendered in MathML at pentagon.xml There is more detail at proof.txt where symmetries are not assumed. The expressions are summarized at summary.txt . The circle variable above is the radius from the center of the solid of the circle inscribed in the pentagon face .