Tetradecahedron
Encyclopedia
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.htmlhttp://bbs.sachina.pku.edu.cn/stat/math_world/math/t/t099.htm No difference in meaning is ascribed.http://mathworld.wolfram.com/Tetrakaidecahedron.htmlhttp://bbs.sachina.pku.edu.cn/stat/math_world/math/t/t117.htm. 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:
Polyhedron
In elementary geometry a polyhedron is a geometric solid in three dimensions with flat faces and straight edges...
with 14 faces
Face (geometry)
In geometry, a face of a polyhedron is any of the polygons that make up its boundaries. For example, any of the squares that bound a cube is a face of the cube...
. There are numerous topologically distinct forms of a tetradecahedron, with many constructible entirely with regular polygon
Regular polygon
A regular polygon is a polygon that is equiangular and equilateral . Regular polygons may be convex or star.-General properties:...
faces.
A tetradecahedron is sometimes called a tetrakaidecahedron.http://mathworld.wolfram.com/Tetradecahedron.htmlhttp://bbs.sachina.pku.edu.cn/stat/math_world/math/t/t099.htm No difference in meaning is ascribed.http://mathworld.wolfram.com/Tetrakaidecahedron.htmlhttp://bbs.sachina.pku.edu.cn/stat/math_world/math/t/t117.htm. The interposition of "kai
Kai (conjunction)
Kai is a conjunction in Greek , Coptic and, under the form kaj, Esperanto.Kai is the most frequent word in any Greek text and thus used by statisticians to assess authorship of ancient manuscripts .-Kai ligature:Because of its frequent occurrence, kai is sometimes abbreviated in Greek...
" probably is due to its meaning in Greek language
Greek language
Greek is an independent branch of the Indo-European family of languages. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. Its writing system has been the Greek alphabet for the majority of its history;...
as a Grammatical conjunction
Grammatical conjunction
In grammar, a conjunction is a part of speech that connects two words, sentences, phrases or clauses together. A discourse connective is a conjunction joining sentences. This definition may overlap with that of other parts of speech, so what constitutes a "conjunction" must be defined for each...
(meaning the same as "and" in the English language
English language
English is a West Germanic language that arose in the Anglo-Saxon kingdoms of England and spread into what was to become south-east Scotland under the influence of the Anglian medieval kingdom of Northumbria...
).
An incomplete list of forms includes:
- Tetradecahedra having all regular polygonRegular polygonA regular polygon is a polygon that is equiangular and equilateral . Regular polygons may be convex or star.-General properties:...
al faces (all exist in irregular-faced forms as well):- Archimedean solidArchimedean solidIn geometry an Archimedean solid is a highly symmetric, semi-regular convex polyhedron composed of two or more types of regular polygons meeting in identical vertices...
s:- CuboctahedronCuboctahedronIn geometry, a cuboctahedron is a polyhedron with eight triangular faces and six square faces. A cuboctahedron has 12 identical vertices, with two triangles and two squares meeting at each, and 24 identical edges, each separating a triangle from a square. As such it is a quasiregular polyhedron,...
(8 equilateral triangles, 6 squaresSquare (geometry)In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles...
) - Truncated cubeTruncated cubeIn geometry, the truncated cube, or truncated hexahedron, is an Archimedean solid. It has 14 regular faces , 36 edges, and 24 vertices....
(8 equilateral triangles, 6 octagons) - Truncated octahedronTruncated octahedronIn geometry, the truncated octahedron is an Archimedean solid. It has 14 faces , 36 edges, and 24 vertices. Since each of its faces has point symmetry the truncated octahedron is a zonohedron....
(6 squares, 8 regular hexagons)
- Cuboctahedron
- PrismsPrism (geometry)In geometry, a prism is a polyhedron with an n-sided polygonal base, a translated copy , and n other faces joining corresponding sides of the two bases. All cross-sections parallel to the base faces are the same. Prisms are named for their base, so a prism with a pentagonal base is called a...
and antiprismAntiprismIn geometry, an n-sided antiprism is a polyhedron composed of two parallel copies of some particular n-sided polygon, connected by an alternating band of triangles...
s:- Dodecagonal prismDodecagonal prismIn geometry, the dodecagonal prism is the tenth in an infinite set of prisms, formed by square sides and two regular dodecagon caps.If faces are all regular, it is a semiregular polyhedron.- Use :...
(12 squares, 2 regular dodecagonDodecagonIn geometry, a dodecagon is any polygon with twelve sides and twelve angles.- Regular dodecagon :It usually refers to a regular dodecagon, having all sides of equal length and all angles equal to 150°...
s) - Hexagonal antiprismHexagonal antiprismIn geometry, the hexagonal antiprism is the 4th in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps.If faces are all regular, it is a semiregular polyhedron.- See also :* Set of antiprisms...
(12 equilateral triangles, 2 regular hexagons)
- Dodecagonal prism
- Johnson solidJohnson solidIn geometry, a Johnson solid is a strictly convex polyhedron, each face of which is a regular polygon, but which is not uniform, i.e., not a Platonic solid, Archimedean solid, prism or antiprism. There is no requirement that each face must be the same polygon, or that the same polygons join around...
s:- J18: Elongated triangular cupolaElongated triangular cupolaIn geometry, the elongated triangular cupola is one of the Johnson solids . As the name suggests, it can be constructed by elongating a triangular cupola by attaching a hexagonal prism to its base....
(4 equilateral triangles, 9 squares, 1 regular hexagon) - J27: Triangular orthobicupolaTriangular orthobicupolaIn geometry, the triangular orthobicupola is one of the Johnson solids . As the name suggests, it can be constructed by attaching two triangular cupolas along their bases...
(8 equilateral triangles, 6 squares) - J51: Triaugmented triangular prismTriaugmented triangular prismIn geometry, the triaugmented triangular prism is one of the Johnson solids . As the name suggests, it can be constructed by attaching square pyramids to each of the three equatorial faces of the triangular prism...
(14 equilateral triangles) - J55: Parabiaugmented hexagonal prismParabiaugmented hexagonal prismIn geometry, the parabiaugmented hexagonal prism is one of the Johnson solids .The 92 Johnson solids were named and described by Norman Johnson in 1966.-External links:**...
(8 equilateral triangles, 4 squares, 2 regular hexagons) - J56: Metabiaugmented hexagonal prismMetabiaugmented hexagonal prismIn geometry, the metabiaugmented hexagonal prism is one of the Johnson solids .The 92 Johnson solids were named and described by Norman Johnson in 1966.-External links:**...
(8 equilateral triangles, 4 squares, 2 regular hexagons) - J65: Augmented truncated tetrahedronAugmented truncated tetrahedronIn geometry, the augmented truncated tetrahedron is one of the Johnson solids . It is created by attaching a triangular cupola to one hexagonal face of an truncated tetrahedron.-External links:**...
(8 equilateral triangles, 3 squares, 3 regular hexagons) - J86: SphenocoronaSphenocoronaIn geometry, the sphenocorona is one of theJohnson solids .It is one of the elementary Johnson solids that do not arise from "cut and paste" manipulations of the Platonic and Archimedean solids....
(12 equilateral triangles, 2 squares) - J91: BilunabirotundaBilunabirotundaIn geometry, the bilunabirotunda is one of the Johnson solids . It is one of the elementary Johnson solids that do not arise from "cut and paste" manipulations of the Platonic and Archimedean solids....
(8 equilateral triangles, 2 squares, 4 regular pentagons)
- J18: Elongated triangular cupola
- Archimedean solid
- Tetradecahedra having at least one irregular face:
- Heptagonal dipyramid (14 triangles) (see Dipyramid)
- Heptagonal trapezohedron (14 kitesKite (geometry)In Euclidean geometry a kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are next to each other. In contrast, a parallelogram also has two pairs of equal-length sides, but they are opposite each other rather than next to each other...
) (see TrapezohedronTrapezohedronThe n-gonal trapezohedron, antidipyramid or deltohedron is the dual polyhedron of an n-gonal antiprism. Its 2n faces are congruent kites . The faces are symmetrically staggered.The n-gon part of the name does not reference the faces here but arrangement of vertices around an axis of symmetry...
) - Tridecagonal pyramid (13 triangles, 1 regular tridecagon) (see Pyramid (geometry)Pyramid (geometry)In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle. It is a conic solid with polygonal base....
) - Dissected regular icosahedron (the vertex figure of the grand antiprismGrand antiprismIn geometry, the grand antiprism or pentagonal double antiprismoid is a uniform polychoron bounded by 320 cells: 20 pentagonal antiprisms, and 300 tetrahedra. It is an anomalous, non-Wythoffian uniform polychoron, discovered in 1965 by Conway and Guy.- Alternate names :* Pentagonal double...
) (12 equilateral triangles and 2 trapezoidTrapezoidIn Euclidean geometry, a convex quadrilateral with one pair of parallel sides is referred to as a trapezoid in American English and as a trapezium in English outside North America. A trapezoid with vertices ABCD is denoted...
s) - Hexagonal truncated trapezohedronHexagonal truncated trapezohedronThe hexagonal truncated trapezohedron is the fourth in an infinite series of truncated trapezohedron polyhedra. It has 12 pentagon and 2 hexagon faces....
: (12 pentagonPentagonIn geometry, a pentagon is any five-sided polygon. A pentagon may be simple or self-intersecting. The sum of the internal angles in a simple pentagon is 540°. A pentagram is an example of a self-intersecting pentagon.- Regular pentagons :In a regular pentagon, all sides are equal in length and...
s, 2 hexagons)
Includes an optimal space-filling shape in foams (see Weaire-Phelan structureWeaire-Phelan structureIn geometry, the Weaire–Phelan structure is a complex 3-dimensional structure representing an idealised foam of equal-sized bubbles. In 1993, Trinity College Dublin physicist Denis Weaire and his student Robert Phelan found that in computer simulations of foam, this structure was a better...
) and in the crystal structure of Clathrate hydrateClathrate hydrateClathrate hydrates are crystalline water-based solids physically resembling ice, in which small non-polar molecules or polar molecules with large hydrophobic moieties are trapped inside "cages" of hydrogen bonded water molecules...
(see illustration, next to label 51262)
See also
- Császár polyhedronCsászár polyhedronIn geometry, the Császár polyhedron is a nonconvex polyhedron, topologically a toroid, with 14 triangular faces.This polyhedron has no diagonals; every pair of vertices is connected by an edge. The seven vertices and 21 edges of the Császár polyhedron form an embedding of the complete graph K_7...
- A nonconvex tetradecahedron of all triangle faces - PermutohedronPermutohedronIn mathematics, the permutohedron of order n is an -dimensional polytope embedded in an n-dimensional space, the vertices of which are formed by permuting the coordinates of the vector .-History:According to , permutohedra were first studied by...