Tetradecahedron

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.

A tetradecahedron is sometimes called a tetrakaidecahedron. [http://mathworld.wolfram.com/Tetradecahedron.html] [http://bbs.sachina.pku.edu.cn/stat/math_world/math/t/t099.htm] No difference in meaning is ascribed. [http://mathworld.wolfram.com/Tetrakaidecahedron.html] [http://bbs.sachina.pku.edu.cn/stat/math_world/math/t/t117.htm] . The interposition of "kai" [http://en.wikipedia.org/wiki/Kai_(conjunction)] 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:
***J₁₈: Elongated triangular cupola (4 equilateral triangles, 9 squares, 1 regular hexagon)
***J₂₇: Triangular orthobicupola (8 equilateral triangles, 6 squares)
***J₅₁: Triaugmented triangular prism (14 equilateral triangles)
***J₅₅: Parabiaugmented hexagonal prism (8 equilateral triangles, 4 squares, 2 regular hexagons)
***J₅₆: Metabiaugmented hexagonal prism (8 equilateral triangles, 4 squares, 2 regular hexagons)
***J₆₅: Augmented truncated tetrahedron (8 equilateral triangles, 3 squares, 3 regular hexagons)
***J₈₆: Sphenocorona (12 equilateral triangles, 2 squares)
***J₉₁: 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 5¹²6²)

ee also

*Permutohedron

External links

*MathWorld | urlname=Tetradecahedron | title=Tetradecahedron