The conical sundial from the museum Thyrrheion is found to be designed with cardinal parameters
geographical latitude ϕ = arc tan(3/5) = 30°57′50″
half cone angle α = arc tan(4/9) = 23°57′45″
radius at equinox r0 = 4 unciae = 98.7mm (pes monetalis)
position of the cone tip h = 18 unciae = 444.3 mm
The half cone angle is equal to the angle of the ecliptic which leads to the special case of a conical sundial with the associated sphere being tangent at the day line of the winter solstice. The ratio of sides in the generating triangle 4:9 may thus be interpreted as an approximation for the angle of ecliptic.
The place of finding (operation) is 10° North of the intended latitude (design). The error of the sundial's indications due to the displacement are analyzed.