mathematics – Lights-out variant on a tetrahedron

You have a tetrahedron whose faces are covered in 4 × 4 triangular grids. Each triangular cell has a light and a switch that toggles that light and the three edge-adjacent lights. The blue dots indicate lights that are ON. For the configurations below, answer the following questions.

1. Can all the lights be turned OFF?
2. If not, what’s the minimal number of lights that remain ON?