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 △PQR.) How many of these triangles are equilateral and contain P as a vertex?<spanclass=′latex−bold′>(A)</span>0<spanclass=′latex−bold′>(B)</span>1<spanclass=′latex−bold′>(C)</span>2<spanclass=′latex−bold′>(D)</span>3<spanclass=′latex−bold′>(E)</span>6
[asy]
unitsize(4);
pair P,Q,R,S,T,U,V,W;
P=(0,30); Q=(30,30); R=(40,40); S=(10,40); T=(10,10); U=(40,10); V=(30,0); W=(0,0);
draw(W--V); draw(V--Q); draw(Q--P); draw(P--W); draw(T--U); draw(U--R); draw(R--S); draw(S--T); draw(W--T); draw(P--S); draw(V--U); draw(Q--R);
dot(P);
dot(Q);
dot(R);
dot(S);
dot(T);
dot(U);
dot(V);
dot(W);
label("P",P,NW);
label("Q",Q,NW);
label("R",R,NE);
label("S",S,N);
label("T",T,NE);
label("U",U,NE);
label("V",V,SE);
label("W",W,SW);
[/asy] AMC 8geometry3D geometry2024 AMC 8