Let's plot the given points on a coordinate plane and graph the parallelogram.

To determine the most precise name for our parallelogram, let's review the definitions of the different types of parallelograms.

Parallelogram	Definition
Rhombus	Parallelogram with four congruent sides
Rectangle	Parallelogram with four right angles
Square	Parallelogram with four congruent sides and four right angles

Now, let's find the slopes of the sides using the Slope Formula.

Side	Points	$\frac{y _{2} - y _{1}}{x _{2} - x _{1}}$	Simplify
$\overline{O P}$	$O (0, 0),$ $P (- 1, 2)$	$\frac{2 - 0}{- 1 - 0}$	$- 2$
$\overline{P T}$	$P (- 1, 2),$ $T (3, 2)$	$\frac{2 - 2}{3 - ( - 1 )}$	$0$
$\overline{T S}$	$T (3, 2),$ $S (4, 0)$	$\frac{0 - 2}{4 - 3}$	$- 2$
$\overline{S O}$	$S (4, 0),$ $O (0, 0)$	$\frac{0 - 0}{0 - 4}$	$0$

We can tell that the consecutive sides are not perpendicular, as their slopes are not opposite reciprocals.

- 2 \cdot 0 \neq = - 1

Since rectangles and squares have perpendicular sides, our parallelogram can only be rhombus or none of the given types of parallelograms. To check if it is a rhombus, we can find the lengths of its sides using the Distance Formula.

Side	Points	$(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}$	Simplify
$\overline{O P}$	$O (0, 0),$ $P (- 1, 2)$	$(- 1 - 0)^{2} + (2 - 0)^{2}$	$5$
$\overline{P T}$	$P (- 1, 2),$ $T (3, 2)$	$(3 - (- 1))^{2} + (2 - 2)^{2}$	$4$
$\overline{T S}$	$T (3, 2),$ $S (4, 0)$	$(4 - 3)^{2} + (0 - 2)^{2}$	$5$
$\overline{S O}$	$S (4, 0),$ $O (0, 0)$	$(0 - 4)^{2} + (0 - 0)^{2}$	$4$

Our parallelogram does not have four congruent sides. Therefore, the given parallelogram is not a rhombus and moreover it is none of the given types of parallelograms.

Exercise