No: [asy][asy] pair O = (0,0), A = dir(90), B = dir(-60), C = dir(-120), D = A+B-O, E = A+C-O ; dot(O); dot(A); dot(B); dot(C); dot(D); dot(E); draw(O--A--D--B--cycle, red); draw(O--A--E--C--cycle, red); draw(O--C--B--cycle, red); path c1 = circle(E,1), c2 = circle(B,1); draw(c1, blue); draw(c2, blue); [/asy][/asy]

^I don't understand this solution

Vertices would have to stack to do it $\implies\text{not possible}. $

Can someone explain statement of the problem ?

No, because at least two vertices are in the same position