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A tetradecahedron is a polyhedron with 14 faces. There are numerous topologically distinct forms of a tetradecahedron, with many constructible entirely with regular polygon faces.## See also

## External links

A tetradecahedron is sometimes called a tetrakaidecahedron. No difference in meaning is ascribed. The interposition of "kai" probably is due to its meaning in Greek language as a Grammatical conjunction (meaning the same as "and" in the English language).

An incomplete list of forms includes:

- Tetradecahedra having all regular polygonal faces (all exist in irregular-faced forms as well):
- Archimedean solids:
- Cuboctahedron (8 equilateral triangles, 6 squares)
- Truncated cube (8 equilateral triangles, 6 octagons)
- Truncated octahedron (6 squares, 8 regular hexagons)
- Prisms and antiprisms:
- Dodecagonal prism (12 squares, 2 regular dodecagons)
- Hexagonal antiprism (12 equilateral triangles, 2 regular hexagons)
- Johnson solids:
- J
_{18}: Elongated triangular cupola (4 equilateral triangles, 9 squares, 1 regular hexagon) - J
_{27}: Triangular orthobicupola (8 equilateral triangles, 6 squares) - J
_{51}: Triaugmented triangular prism (14 equilateral triangles) - J
_{55}: Parabiaugmented hexagonal prism (8 equilateral triangles, 4 squares, 2 regular hexagons) - J
_{56}: Metabiaugmented hexagonal prism (8 equilateral triangles, 4 squares, 2 regular hexagons) - J
_{65}: Augmented truncated tetrahedron (8 equilateral triangles, 3 squares, 3 regular hexagons) - J
_{86}: Sphenocorona (12 equilateral triangles, 2 squares) - J
_{91}: Bilunabirotunda (8 equilateral triangles, 2 squares, 4 regular pentagons) - Tetradecahedra having at least one irregular face:
- Heptagonal dipyramid (14 triangles) (see Dipyramid)
- Heptagonal trapezohedron (14 kites) (see Trapezohedron)
- Tridecagonal pyramid (13 triangles, 1 regular tridecagon) (see Pyramid (geometry))
- Dissected regular icosahedron (the vertex figure of the grand antiprism) (12 equilateral triangles and 2 trapezoids)
- Hexagonal truncated trapezohedron: (12 pentagons, 2 hexagons)

Includes an optimal space-filling shape in foams (see Weaire-Phelan structure) and in the crystal structure of Clathrate hydrate (see illustration, next to label 5^{12}6^{2})

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Last updated on Friday August 29, 2008 at 09:54:51 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Friday August 29, 2008 at 09:54:51 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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