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.[1][2] No difference in meaning is ascribed.[3][4] 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.[5] The polyhedron can also be found in soap bubbles and in sintered ceramics, due to its ability to tesselate in 3D space.[6][7]

Convex

There are 1,496,225,352 topologically distinct convex tetradecahedra, excluding mirror images, having at least 9 vertices.[8] (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

An incomplete list of forms includes:

Tetradecahedra having all regular polygonal faces (all exist in irregular-faced forms as well):

Tetradecahedra having at least one irregular face:

See also

References

  1. ^ Weisstein, Eric W. "Tetradecahedron". MathWorld. Retrieved 11 March 2024.
  2. ^ "Tetradecahedron". Archived from the original on 18 July 2011. Retrieved 29 October 2007.
  3. ^ Weisstein, Eric W. "Tetrakaidecahedron". MathWorld. Retrieved 11 March 2024.
  4. ^ "Tetrakaidecahedron". Archived from the original on 28 September 2011. Retrieved 29 October 2007.
  5. ^ Yokouchi, Mariko; Atsugi, Toru; Logtestijn, Mark van; Tanaka, Reiko J.; Kajimura, Mayumi; Suematsu, Makoto; Furuse, Mikio; Amagai, Masayuki; Kubo, Akiharu (2016). "Epidermal cell turnover across tight junctions based on Kelvin's tetrakaidecahedron cell shape". eLife. 5. doi:10.7554/eLife.19593. PMC 5127639. PMID 27894419.
  6. ^ "Most space Filling Structure in the World! – Tetradecahedron". Ardent Metallurgist. 2020-07-26. Retrieved 2022-11-15.
  7. ^ Wey, Ming-Yen; Tseng, Hui-Hsin; Chiang, Chian-kai (2014-03-01). "Improving the mechanical strength and gas separation performance of CMS membranes by simply sintering treatment of α-Al2O3 support". Journal of Membrane Science. 453: 603–613. doi:10.1016/j.memsci.2013.11.039. ISSN 0376-7388.
  8. ^ Counting polyhedra
  9. ^ "New Pound Coin | the Royal Mint".