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

The geometry of an octagon can be vastly different depending on its construction. A solid octagon boasts a complete, continuous surface, formed by eight interconnected sides and corners. In contrast, a hollow octagon possesses open space within its structure. This distinction has significant implications for the octagon's properties, including its