Check the vertices. I will help out for the triangle.

(shifted down one unit).

(shifted down two units and to the right one unit).

(shifted up one unit).

The line segment between and is given by the line . So that edge is going to:

which is the line , so a slanted line between (-1,-1) and (1,1).

The line segment between and is given by the line . So that edge is going to:

So that edge is now horizontal going from (-1,-1) to (1,-1).

The line segment between and is given by the line . So that edge is going to:

so that edge is now a vertical line going from (1,-1) to (1,1). In other words, the triangle is rotated 225 degrees = radians and stretched by a factor of .

Consider the unit circle. Every point of the unit circle is given by . So,

Now, points on the unit sphere have the property that . Now,

So, you now have a circle of radius . Seeing a pattern?