2023 AMC 10A Problem 18

A rhombic dodecahedron is a solid with 12 congruent rhombus faces. At every vertex, 3 or 4 edges meet, depending on the vertex. How many vertices have exactly 3 edges meeting?

\textbf{(A)} 5 \qquad \textbf{(B)} 6 \qquad \textbf{(C)} 7 \qquad \textbf{(D)} 8 \qquad \textbf{(E)} 9

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