Tetrahedron

Definition: Tetrahedron

Tetrahedron

Noun

1. Any polyhedron having four plane faces.

Etymology: Tetrahedron \Tet`ra*he"dron\, noun. [Tetra- Greek expression seat, base, from to sit.]. (Websters 1913)

Specialty Definitions: Tetrahedron

Domain	Definitions
Mining	An isometric crystal form of four faces, each an equilateral triangle; thealternate faces of an octahedron. Adj: tetrahedral. (references)
Transportation	A device, normally found at uncontrolled airports, used as a landing direction indicator. Source: European Union. (references)
Source: compiled by the editor from various references; see credits.

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Specialty Definition: Tetrahedron

(From Wikipedia, the free Encyclopedia)

A tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex. A regular tetrahedron is one in which the four triangles are regular, or "equilateral," and is one of the Platonic solids.

A tetrahedron is a 3-simplex.

Tetrahedra are a special type of triangular pyramid and are self-dual. Canonical coordinates of the tetrahedron are (1, 1, 1), (-1, -1, 1), (-1, 1, -1) and (1, -1, -1). A regular tetrahedron can be embedded inside a cube in two ways such that each vertex is a vertex of the cube, and each edge is a diagonal of one of the cube's faces. The volume of this tetrahedron is 1/3 the volume of the cube. Taking both tetrahedra within a single cube gives a regular polyhedral compound called the stella octangula, whose interior is an octahedron. Inscribing tetrahedra inside the regular compound of five cubes gives two more regular compounds, containing five and ten tetrahedra.

Regular tetrahedra can't tile space by themselves, although it seems likely enough that Aristotle reported it was possible. In fact, octahedra are necessary to fill some of the gaps. This is one of the five Andreini tessellations, and is a limiting case of another, a tiling involving tetrahedra and truncated tetrahedra.

The volume of an irregular tetrahedron, given its verticies a, b, c and d, is (1/6)·|det(a-b, b-c, c-d)|, or any other combination of pairs of verticies that form a simply connected graph. (This works for regular tetrahedrons too.)

Like all platonic solids, archimedean solids and a lot (maybe all, not sure) of convex polyhedra, a tetrahedron can be folded from a single sheet of paper.

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Tetrahedron."

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Synonyms within Context: Tetrahedron

Context	Synonyms within Context (source: adapted from Roget's Thesaurus).
Angularity	Platonic bodies; cube, rhomboid; tetrahedron, pentahedron, hexahedron, octahedron, dodecahedron, icosahedron, eicosahedron; prism, pyramid; parallelopiped; curb roof, gambrel roof, mansard roof.
Four	Tetrahedron.
Source: adapted from Roget's Thesaurus.

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Crosswords: Tetrahedron

English words defined with "tetrahedron": Cuproid ♦ Deltohedron ♦ Hemihedral, Hemihedron ♦ Platonic bodies ♦ regular polyhedron, regular tetrahedron ♦ Tetrahedral. (references)

Specialty definitions using "tetrahedron": disphenoid ♦ silicate minerals, silicon-oxygen tetrahedron. (references)

Etymologies containing "tetrahedron": Tetrahedral. (references)

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Commercial Usage: Tetrahedron

Domain	Title
Books	Tetrahedron (reference) (more book examples)

Periodicals	Bioorganic & Medicinal Chemistry C-w Tetrahedron Letters (reference) Tetrahedron - Combination (reference) Tetrahedron Letters (reference) Tetrahedron Letters - Microfiche (reference) (more periodical examples)
Source: compiled by the editor from various references; see credits.

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Photo Album: Tetrahedron

Thumbnail	Description & Credit
	"Tetrahedron" by Владимир Смирнов (Vladimir Smirnov). These platonic solids illustrate a clever use of the absolute value function.
Source: compiled by the editor from various references; see credits.

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Usage Frequency: Tetrahedron

"Tetrahedron" is generally used as a noun (singular) -- approximately 100.00% of the time. "Tetrahedron" is used about 14 times out of a sample of 100 million words spoken or written in English. Its rank is based on over 700,000 words used in the English language. Some parts-of-speech are not covered due to the samples used by the British National Corpus. (note: percents less than one-hundredth of one percent have been omitted)

Parts of Speech	Percent	Usage per 100 Million Words	Rank in English
Noun (singular)	100%	14	93,893

Source: compiled by the editor from several corpora; see credits.

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Expressions: Tetrahedron

Expressions using "tetrahedron": landing tetrahedron ♦ regular tetrahedron. Additional references.
Source: compiled by the editor from various references; see credits.

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Frequency of Internet Keywords: Tetrahedron

The following statistics estimate the number of searches per day across the major English-language search engines as identified by various trade publications. Hyperlinks lead to commercial use of the expression at Amazon.com.

Expression	Frequency per Day
tetrahedron	123
letter tetrahedron	20
fire tetrahedron	11
kite tetrahedron	11
tetrahedron volume	6
sierpinski tetrahedron	4
star tetrahedron	4
build tetrahedron	3
regular tetrahedron	2
prime tetrahedron	2
tetrahedron truncated	2
shape tetrahedron	2
picture tetrahedron	2
area tetrahedron	2
Source: compiled by the editor from various references; see credits.

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Modern Translations: Tetrahedron

Language		Translations for "tetrahedron"; alternative meanings/domain in parentheses.
Albanian		katërkëndësh (four-cornered, quad, quadrangle, quadrangular, quadrate, quadrilateral, tetragon, tetragonal, trapezium). (various references)

Arabic		‏الرباعي السطوح. (various references)

Bulgarian		четиристен, тетраедър. (various references)

Chinese		四面�" , 四面�" (Tetrahedral). (various references)

Czech		ètyřstìn. (various references)

Danish		tetraeder. (various references)

Dutch		tetraeder (carton, carton of milk, humbug, sachet, tetra-pack), tetraëder, regelmatig viervlak. (various references)

French		tétraèdre. (various references)

German		Tetraeder (carton, carton of milk, sachet, tetra-pack). (various references)

Greek		τετράεδρον, τετράεδρο (humbug). (various references)

Hebrew		ארבעון (tetrad). (various references)

Hungarian		tetraéder. (various references)

Italian		tetraedro (humbug). (various references)

Japanese Kanji		四面�" . (various references)

Japanese Katakana		しめ�"たい. (various references)

Manx		tetraheedran. (various references)

Pig Latin		etrahedrontay

Portuguese		tetraedro (humbug). (various references)

Russian		четырехгранник (tetrahedra). (various references)

Serbo-Croatian		tetraedar. (various references)

Spanish		tetraedro (humbug). (various references)

Swedish		tetraeder (triakistetrahedron, trigonal tristetrahedron). (various references)

Turkish		dört yüzlü şekil, dört üçgen yüzlü şekil. (various references)

Vietnamese		tứ diện (tetrahedral). (various references)
Source: compiled by the editor from various translation references.

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Derivations & Misspellings: Tetrahedron

Derivations
	Words beginning with "tetrahedron": tetrahedrons. (additional references)
Misspellings
	"Tetrahedron" is suggested in spellcheckers for the following: tetraheadron, tetrahedon. (additional references)
Source: compiled by the editor, based on several corpora (additional references).

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Rhyming with "Tetrahedron"

# of Phoneme Matches	Pronunciation	Word(s) rhyming with "tetrahedron" (pronounced te'truhē"drun)
7	-u h ē" d r u n	octahedron.
6	-h ē" d r u n	polyhedron.
4	-d r u n	cauldron, children, grandchildren, Philodendron, rhododendron, schoolchildren, squadron, stepchildren.
3	-r u n	apron, aspirin, Baron, barren, brethren, Buran, Chevron, citron, doctrine, fibrin, foreign, garron, giron, heron, intron, Marron, matron, patron, perron, saffron, siren, sovereign, sovran, Warren.
Source: compiled by the editor (additional references); see credits.

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Anagrams: Tetrahedron

Scrabble® Enable2K-Verified Anagrams
	Words within the letters "a-d-e-e-h-n-o-r-r-t-t"
	-2 letters: dethroner.
	-3 letters: adherent, attender, attorned, dehorner, dethrone, detonate, hardener, headnote, nattered, neatherd, rattened, rattener, reharden, rethread, retorted, rottener, threader, threated, threaten, threnode, throated.
	-4 letters: adherer, adorner, another, dentate, earthed, earthen, entreat, erodent, hearted, hearten, hoarder, horrent, norther, notated, ratteen, readorn, reheard, retread, retreat, rotated, ternate, terrane, tetrode, theater, theatre, thereat, thereon, thereto, thorned, throned, torrent, treader, treated, treater, trothed.
	-5 letters: adhere, adorer, aether, anteed, anther, ardent, atoned, atoner, attend, attorn, darner, darter, dearer, dearth, dehorn, dehort, denote, derate, detent, donate, dotter, droner, earned, earner, endear, entera, errand, errant, ethane, hadron, hanted, harden, harder, hatred, hatted, hatter, header, hearer, heated, heater, hented, herder, hereat, hereon, hereto, hetero, horned, hornet, hotted, hotter, natter, neared, nearer, neater, nether, netted, netter, notate, nother, orated, ornate, ranted, ranter, rather, ratted, ratten, ratter, ratton, reader, reared, redate, redear, redone, reearn, rehear, reheat, render, rented, renter, reread, retard, retear, retore, retorn, retort, retted, rhetor, roared, rodent, rotate, rotted, rotten, rotter, tarred, tarted, tarter, teared, tearer, teated, tender, tented, tenter, teredo, terrae, terret, tether, tetrad, thenar, thread, threat, throat, throne, torten, tother, trader.
	Words containing the letters "a-d-e-e-h-n-o-r-r-t-t"
	+1 letter: tetrahedrons.
Source: compiled by the editor from various references; see credits. SCRABBLE® is a registered trademark. All intellectual property rights in and to the game are owned in the U.S.A and Canada by Hasbro Inc., and throughout the rest of the world by J.W. Spear & Sons Limited of Maidenhead, Berkshire, England, a subsidiary of Mattel Inc. Mattel and Spear are not affiliated with Hasbro.