Hexahedron

Hexaeder [ hɛksaeːdər ]. From the Greek hexáedron , "hexahedron" generally refers to a polyhedron with six boundary surfaces. In particular, especially in connection with Platonic solids , it is about the regular (6 congruent surfaces) hexahedron or the cube .

Number of hexahedra

There are infinitely many convex hexahedra. If one differentiates only according to the structure (more precisely: according to the underlying edge graph ), for example, a parallelepiped or a truncated pyramid with a four-sided base cannot be distinguished from a cube, but all of these cannot be distinguished from a pyramid with a pentagonal base. In this sense, there are only seven different types of convex hexahedra.

cube Areas: 4,4,4,4,4,4 8 corners 12 edges	Pyramid with a pentagonal base Areas: 5,3,3,3,3,3 6 corners 10 edges	Areas: 5,4,4,3,3,3 7 corners 11 edges	Areas: 5,5,4,4,3,3 8 corners 12 edges
Double tetrahedron Areas: 3,3,3,3,3,3 5 corners 9 edges	Areas: 4,4,4,4,3,3 7 corners 11 edges	This body shows chirality: There is a “left-handed” and a “right-handed” variant, which emerge from each other through plane reflection . Areas: 4,4,3,3,3,3 6 corners 10 edges

If one also considers non-convex hexahedra, the following three other types are added.

Areas: 4,4,3,3,3,3 6 corners 10 edges

Areas: 5,5,3,3,3,3 7 corners 11 edges

Areas: 6,6,3,3,3,3 8 corners 12 edges

Hexahedra in chemistry

• An organic compound that is built up like a cube is Cuban, named after the English cube .
• Cubic crystal systems appear when describing the geometric structure of crystals, such as table salt ( sodium chloride structure ).

literature

• Proof of the existence of exactly seven convex hexahedra: Anatole Beck, Michael Bleicher, Donald Crowe: Excursions into Mathematics . 1969, p. 29-30 .

Web links

Commons : Hexahedron  - collection of images, videos and audio files

Wiktionary: Hexahedron  - explanations of meanings, word origins, synonyms, translations

Individual evidence

1. ↑ Martin Gardner : Puzzle games from other planets . Hugendubel, Munich 1986, ISBN 3-88034-295-4 , p. 134 .