Octadecahedron

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In geometry, an octadecahedron (or octakaidecahedron) is a polyhedron with 18 faces. No octadecahedron is regular; hence, the name is ambiguous.

In chemistry, the octadecahedron commonly refers to a specific structure, the edge-contracted icosahedron, formed from a regular icosahedron, with one edge contracted, with C2v symmetry it is adopted by the closo-boranate [B11H11]2−.

Convex[edit]

There are 107,854,282,197,058 topologically distinct convex octadecahedra, excluding mirror images, having at least 11 vertices.[1] (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.)

Examples[edit]

The most familiar octadecahedra are the heptadecagonal pyramid, hexadecagonal prism, and the octagonal antiprism. The hexadecagonal prism and the octagonal antiprism are uniform polyhedra, with regular bases and square or equilateral triangular sides. Four more octadecahedra are also found among the Johnson solids: the square gyrobicupola, the square orthobicupola, the elongated square cupola (also known as the diminished rhombicuboctahedron), and the sphenomegacorona. Four Johnson solids have octadecahedral duals: the elongated triangular orthobicupola, the elongated triangular gyrobicupola, the gyroelongated triangular bicupola, and the triangular hebesphenorotunda.

Octagonal antiprism.png
Octagonal antiprism
Square gyrobicupola.png
Square gyrobicupola
Sphenomegacorona.png
Sphenomegacorona

In addition, some uniform star polyhedra are also octadecahedra:

Antiprism 8-3.png
Octagrammic antiprism
Antiprism 8-5.png
Octagrammic crossed-antiprism
Small rhombihexahedron.png
Small rhombihexahedron
Small dodecahemidodecahedron.png
Small dodecahemidodecahedron
Great rhombihexahedron.png
Great rhombihexahedron
Great dodecahemidodecahedron.png
Great dodecahemidodecahedron

References[edit]