octodecahedral

An octodecahedron is a polyhedron with 18 faces, 36 edges, and 24 vertices. It is a type of Archimedean solid, which means it is one of the 13 convex polyhedra whose faces are regular polygons of two or more different types. The octodecahedron is composed of 8 hexagonal faces and 10 square faces. Each vertex of an octodecahedron is the meeting point of one hexagon and two squares.

The octodecahedron can be constructed by truncating the vertices of a cube, resulting in a polyhedron with 18 faces. Alternatively, it can be derived from the great rhombicuboctahedron by truncating its vertices. The octodecahedron is also known as the truncated cube or the truncated hexahedron.

In geometry, the octodecahedron is notable for its symmetrical properties and its relationship to other polyhedra. It is a dual polyhedron to the rhombic dodecahedron, meaning that the vertices of one correspond to the faces of the other, and vice versa. The octodecahedron is also a member of the Archimedean family of polyhedra, which are known for their uniform face types and symmetrical structures.