2024 AMC 8 Problem 20

Any three vertices of the cube PQRSTUVW, shown in the figure below, can be connected to form a triangle. (For example, vertices P, Q, and R can be connected to form isosceles \bigtriangleup PQR.) How many of these triangles are equilateral and contain P as a vertex?

\textbf{(A)} 0 \qquad \textbf{(B)} 1 \qquad \textbf{(C)} 2 \qquad \textbf{(D)} 3 \qquad \textbf{(E)} 6

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.