Freeth's supertrisectrix is the strophoid of a limaçon trisectrix with the center of its generating circle as pole and its double point as fixed point (Lockwood 1967, p. 136).
Choose a scale 
,
pole 
, and fixed point 
. The generating limaçon
trisectrix can then be parametrized as 
.
For 
, the strophoid
consists of the two points on the line 
whose distance from 
equals 
,
together with their limiting points. Both branches are
traced by the parametric equations
 |  |  |
(1)
|
 |  |  |
(2)
|
where 
(Mangaldan 2021). Equivalently, the polar equation
is
 |
(3)
|
for 
.
The curve can be used to construct a regular hendecagon. Its intersection 
with the perpendicular
bisector of 
gives an isosceles triangle 
whose base angles are 
and whose vertex angle is 
("Appendix" 1879).
