MHB Arrange 4-Gon Figures: Find Descendants w/o Descendants

[roni1]

If I arrange the 4-gon polygon by order as:
a rectangle is a descendant of parallelogram and a square is a descendant of rectangle.
What are the descendant that no have any descendants (in 4-gon figures)?

 

[Greg]

What are the rules for determining descendants?

 

[roni1]

the property that the figure has like the father but you can say that the son have but so "fathers" (let call them father brothers) haven't.

square is the son of rectangle.

Not every rectangle can be a square,
But every square is a rectangle.
O.K.
The square is the son and the rectangle is the father. The brothers of the rectangle are rectangle that are not square.

 

[Greg]

Then I'd say a square is what your looking for; a square can only be a square.

 

[Olinguito]

If I arrange the 4-gon polygon by order as:
a rectangle is a descendant of parallelogram and a square is a descendant of rectangle.
What are the descendant that no have any descendants (in 4-gon figures)?

Hi roni.

The mathematical term for what you call “descendants” is subsets. Thus, the set of all rectangles is a subset of the set of all parallelograms, and the set of all squares is a subset of the set of all rectangles.

The subset you’re looking for is the set of all squares because the square is the “most symmetrical” of all quadrilaterals – in the sense that its symmetry group has order 8 and no other quadrilateral has a symmetry group of the same or higher order.