if you already have a convex hull of the object, and the case includes corner points, then all you need to do is simplify the case until it has only 6 points.
There are many ways to simplify polygons, for example, you can simply use this simple algorithm used in this answer: How to find the angular coordinates of a rectangle in an image
do
for each point P on the convex hull:
measure its distance to the line AB _
between the point A before P and the point B after P,
remove the point with the smallest distance
repeat until 6 points left
, ,
Ramer-Douglas-Peucker, , openCV cv:: approxPolyDP.
openCV, 6 4