An alternating stack of insulating layers and spacer material layers is formed over a substrate. The spacer material layers are formed as, or are subsequently replaced with, electrically conductive layers. Memory openings and support openings are formed through the alternating stack. The memory openings are arranged in a first hexagonal array having a nearest-neighbor direction that is parallel to a first horizontal direction, and the support openings are arranged in a second hexagonal array having a nearest-neighbor direction that is perpendicular to the first horizontal direction. Memory opening fill structures are formed within a respective one of the memory openings, and support pillar structures within a respective one of the support openings.