Tetradecahedron
image:Space-filling tetrakaidecahedron.png|thumb|right|240px|A tetradecahedron with D2d-symmetry, existing in the Weaire–Phelan structure
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. No difference in meaning is ascribed. The Greek word kai means 'and'. There is evidence that mammalian epidermal cells are shaped like flattened tetrakaidecahedra, an idea first suggested by Lord Kelvin. The polyhedron can also be found in soap bubbles and in sintered ceramics, due to its ability to tesselate in 3D space.
Convex
There are 1,496,225,352 topologically distinct convex tetradecahedra, excluding mirror images, having at least 9 vertices.Examples
An incomplete list of forms includes:Tetradecahedra having all regular polygonal faces :
- Archimedean solids:
- * Cuboctahedron
- * Truncated cube
- * Truncated octahedron
- Prisms and antiprisms:
- * Dodecagonal prism
- * Hexagonal antiprism
- Johnson solids:
- * J18: Elongated triangular cupola
- * J27: Triangular orthobicupola
- * J51: Triaugmented triangular prism
- * J55: Parabiaugmented hexagonal prism
- * J56: Metabiaugmented hexagonal prism
- * J65: Augmented truncated tetrahedron
- * J86: Sphenocorona
- * J91: Bilunabirotunda
- Heptagonal bipyramid
- Heptagonal trapezohedron
- Tridecagonal pyramid
- Dissected regular icosahedron
- Hexagonal truncated trapezohedron:
- Hexagonal bifrustum
- The British £1 coin in circulation from 2017 – with twelve edges and two faces – is an irregular dodecagonal prism, when one disregards the edging and relief features.