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a csonkolt trapezoéderek végtelen halmazának harmadik tagja. Ezeket úgy képezhetjük, hogy egy pentagonális trapezoédert csonkolunk a két tengely-csúcsánál.
<!--The [[stellation]]s of the dodekaéder make up three of the four [[Kepler-Poinsot polyhedra]].
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=== Csúcsok elrendeződése ===
A dodekaéder csúcselrendeződése megegyezik négy nemkonvex [[uniform poliéder]]ével és három ''[[uniform compound]]''éval.
<!--Five [[cube]]s fit within, with their edges as diagonals of the dodekaéder's faces, and together these make up the regular [[polyhedral compound]] of five cubes.
Since two tetrahedra can fit on alternate cube vertices, five and ten tetrahedra can also fit in a dodekaéder. -->
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== További dodekaéderek ==
The term dodekaéder is also used for other [[poliéder|polyhedra]] with twelve faces, most notably the [[rhombic dodekaéder]] which is dual to the [[cuboctahedron]] (an [[Archimedean solid]]) and occurs in nature as a crystal form. The [[Platonic solid]] dodekaéder can be called a ''pentagonal dodekaéder'' or a ''regular dodekaéder'' to distinguish it. The [[pyritohedron]] is an irregular pentagonal dodekaéder.
Other dodekaéderek include:
* [[Uniform poliéder|Uniform polyhedra]]:
* # [[Pentagonal antiprism]] – 10 equilateral triangles, 2 pentagons
* # [[Decagonal prism]] – 10 squares, 2 decagons
* [[Johnson solid]]s (regular faced):
* # [[Pentagonal cupola]] – 5 triangles, 5 squares, 1 pentagon, 1 decagon
* # [[Snub disphenoid]] – 12 triangles
* # [[Elongated square dipyramid]] – 8 triangles and 4 squares
* # [[Metabidiminished icosahedron]] – 10 triangles and 2 pentagons
* Congruent nonregular faced: ([[face-transitive]])
* # [[Hexagonal bipyramid]] – 12 isosceles [[triangle]]s, dual of [[hexagonal prism]]
* # [[Hexagonal trapezohedron]] – 12 [[kite (geometry)|kite]]s, dual of [[hexagonal antiprism]]
* # [[Triakis tetrahedron]] – 12 isosceles [[triangle]]s, dual of [[truncated tetrahedron]]
* # [[Rhombic dodekaéder]] (mentioned above) – 12 [[rhombus|rhombi]], dual of [[cuboctahedron]]
* Other nonregular faced:
* # [[Hendecagon]]al [[pyramid (geometry)|pyramid]] – 11 isosceles triangles and 1 [[polygon|hendecagon]]
* # [[Trapezo-rhombic dodekaéder]] – 6 rhombi, 6 [[trapezoid]]s - dual of [[Triangular orthobicupola]]
* # [[Rhombo-hexagonal dodekaéder]] or ''Elongated dodekaéder'' – 8 rhombi and 4 equilateral [[hexagon]]s.
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== Előfordulás a művészetekben és a kultúrában ==
* Small, hollow bronze [[Roman dodekaéderek]] dating from the 3rd century A.D. have been found in various places in Europe. Their purpose is not certain.
* A dodekaéder sits on the table in [[M. C. Escher]]'s lithograph print "[[Reptiles (M. C. Escher)|Reptiles]]" (1943), and a stellated dodekaéder is used in his "[[Gravitation (M. C. Escher)|Gravitation]]".
* In [[Salvador Dalí]]'s painting of The Sacrament of the Last Supper (1955), the room is a hollow dodekaéder.
* The 20 vertices and 30 edges of a dodekaéder form the [[graph theory|map]] for an early computer game, ''[[Hunt the Wumpus]]''.
* One of the characters in [[The Phantom Tollbooth]], a children's novel from 1961, is named dodekaéder and is a man with 12 faces.
* The dodekaéder was the mysterious power source for an underground city in the [[Doctor Who]] episode [[Meglos]] (1980).
* In the [[Carl Sagan]] book ''[[Contact]]'', the transport device constructed to the plans transmitted by the alien intelligence is dodekaéderekl in shape.
* In the episode [[Blood Feud]] of [[The Simpsons]], [[Lisa Simpson|Lisa]] attempts to teach [[Maggie Simpson|Maggie]] the word ''dodekaéder''.
* "dodekaéder" is the title of a song by [[Aphex Twin]].
* In 2003, an apparent [[periodicity]] in the [[cosmic microwave background]] led to the suggestion, by [http://luth2.obspm.fr/~luminet/eluminet.html Jean-Pierre Luminet] of the [[Observatoire de Paris]] and colleagues, that the [[shape of the Universe]] is a finite dodekaéder, attached to itself by each pair of opposite faces to form a [[Poincaré homology sphere]]. ([http://physicsweb.org/articles/news/7/10/5 "Is the universe a dodekaéder?"], article at PhysicsWeb.) During the following year, astronomers searched for more evidence to support this hypothesis but found none.
* In the Nintendo 64 game [[Paper Mario]], the mountains in the background of Toad Town are dodekaéderek. ([http://www.gamespot.com/pages/image_viewer/frame_lead.php?pid=198849&img=80&sid=undefined] Image of background)
* The save points in the Castlevania games, [[Castlevania: Symphony of the Night]] (for the [[PSX]]) and [[Castlevania: Harmony of Dissonance]] ([[GBA]]) are shaped like dodekaéders.
* If each edge of a dodekaéder is a one-[[Ohm (unit)|ohm]] [[resistor]], the resistance between adjacent vertices is 19/30 ohm, and that between opposite vertices is 7/6 ohm.<ref>{{cite journal | last = Klein | first = Douglas J. | year = 2002 | title = Resistance-Distance Sum Rules | journal = Croatica Chemica Acta | volume = 75 | issue = 2 | pages = 633–649 | url = http://jagor.srce.hr/ccacaa/CCA-PDF/cca2002/v75-n2/CCA_75_2002_633_649_KLEIN.pdf | format = PDF | accessdate = 2006-09-30}}</ref>
* The regular dodekaéder is often used in [[role-playing games]] as a twelve-sided [[dice|die]] ("d12" for short), one of the more common [[dice#Non-cubical dice|polyhedral dice]].
== Hivatkozások ==
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== Lásd még ==
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