Geometric shapes fascinate scientists with their diverse characteristics. Two such intriguing forms are octagonal and hexagonal solids. While both exhibit captivating symmetries, they distinguish in several crucial aspects. An octagon possesses eight sides, while a hexagon has six. This basic distinction influences the number of vertices and faces

When designing geometric shapes, the choice between solid and hollow octagons can significantly impact both their aesthetic appeal and practical applications. Dense octagons, with their completely filled areas, project a sense of strength and permanence. They are often used in architectural designs, logo creation, and artistic renderings to convey