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Ingeometry, anoctadecahedron (oroctakaidecahedron) is apolyhedron with 18faces. No octadecahedron isregular; hence, the name does not commonly refer to one specific polyhedron.
Inchemistry, "the octadecahedron" commonly refers to a specific structure with C2v symmetry, theedge-contracted icosahedron, formed from a regularicosahedron with one edgecontracted. It is the shape of thecloso-boranate ion [B11H11]2−.
There are 107,854,282,197,058 topologically distinctconvex octadecahedra, excluding mirror images, having at least 11 vertices.[2] (Two polyhedra are "topologically distinct" if they have intrinsically different arrangements of faces and vertices, such that it is impossible to distort one into the other simply by changing the lengths of edges or the angles between edges or faces.)
The most familiar octadecahedra are theheptadecagonalpyramid,hexadecagonalprism, and theoctagonal antiprism. The hexadecagonal prism and the octagonal antiprism areuniform polyhedra, withregular bases andsquare orequilateral triangular sides. Four more octadecahedra are also found among theJohnson solids: thesquare gyrobicupola, thesquare orthobicupola, theelongated square cupola (also known as the diminished rhombicuboctahedron), and thesphenomegacorona. Four Johnson solids have octadecahedral duals: theelongated triangular orthobicupola, theelongated triangular gyrobicupola, thegyroelongated triangular bicupola, and thetriangular hebesphenorotunda.Amongnear-miss Johnson solids, thechamfered cube is one notable non-uniform octadecahedron.
 Octagonal antiprism |  Square gyrobicupola |  Sphenomegacorona |  Elongated hexagonal bipyramid |  Chamfered cube |
In addition, someuniform star polyhedra are also octadecahedra:
 Octagrammic antiprism |  Octagrammic crossed-antiprism |  Small rhombihexahedron |  Small dodecahemidodecahedron |  Great rhombihexahedron |  Great dodecahemidodecahedron |