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	~~{{Semireg polyhedra db\|Semireg polyhedron stat table\|tD}}~~		Bryan is usually a celebrity in the producing as well as profession progress initially next to [http://lukebryantickets.pyhgy.com luke bryan meet and greet tickets] his 3rd theatre album, And , is the confirmation. He burst on the scene in 2006 regarding his amazing blend of down-residence accessibility, motion picture legend excellent seems and lyrics, is set t in a main way. The new record Top around the region graph and #2 about the pop graphs, building it the 2nd highest first appearance in those days of 2008 for the region designer. <br><br><br><br>The boy of a , understands perseverance and willpower are key elements in terms of a prosperous profession- . His initially recording, Continue to be Me, created the best hits “All My Buddies “Country and Say” Man,” although his energy, Doin’ Point, identified the performer-about three right No. 3 single people: In addition Calling Is actually a Very good Thing.”<br><br>In the fall of 2003, Tour: Luke & that had an [http://lukebryantickets.flicense.com luke bryan tour tickets 2014] amazing list of , which includes Metropolitan. “It’s much like you are receiving a authorization to visit to a higher level, affirms those musicians that were a part of the Concert toursaround right into a greater amount of designers.” It wrapped as among the most successful tours in the 15-12 months historical past.<br><br>my website ... [http://www.museodecarruajes.org meet and greet luke bryan tickets]
	~~In [[geometry]], the '''truncated dodecahedron'''~~ is ~~an [[Archimedean solid]]. It has 12 regular [[decagon]]al faces, 20 regular [[triangular]] faces, 60 vertices and 90 edges.~~
	~~__TOC__~~

	~~==Geometric relations==~~
	~~This [[polyhedron]] can be formed from~~ a ~~[[dodecahedron]] by [[Truncation (geometry)\|truncating]] (cutting off) the corners so the [[pentagon]] faces become [[decagon]]s and the corners become [[triangle]]s.~~

	~~It is used~~ in the [~~[cell-transitive]] hyperbolic space-filling tessellation, the [[Bitruncation#Self-dual~~ .~~7Bp,q,p~~.~~7D polychora/honeycombs\|bitruncated icosahedral honeycomb]].~~

	~~==Area and volume==~~
	~~The area ''A''~~ and ~~the [[volume]] ''V'' of a truncated dodecahedron of edge length ''a'' are:~~
	~~:<math>A = 5 \left(\sqrt{3}+6\sqrt{5+2\sqrt{5}}\right) a^2 \approx 100.99076a^2</math>~~
	~~:<math>V = \frac{5}{12} \left(99+47\sqrt{5}\right) a^3 \approx 85.0396646a^3</math>~~

	~~==Cartesian coordinates==~~
	~~The following [[Cartesian coordinates]] define the vertices of a [[Truncation (geometry)\|truncated~~]~~] [[dodecahedron]] with edge length 2(τ−1)~~, ~~centered at the origin:<ref>{{mathworld \|title=Icosahedral group \|urlname=IcosahedralGroup}}</ref>~~
	~~:(0, ±1/τ, ±(2+τ))~~
	~~:(±(2+τ), 0, ±1/τ)~~
	~~:(±1/τ, ±(2+τ), 0)~~
	~~:(±1/τ, ±τ, ±2τ)~~
	~~:(±2τ~~, ~~±1/τ, ±τ)~~
	~~:(±τ, ±2τ, ±1/τ)~~
	~~:(±τ, ±2, ±τ<sup>2</sup>)~~
	~~:(±τ<sup>2</sup>, ±τ, ±2)~~
	~~:(±2, ±τ<sup>2</sup>, ±τ)~~

	~~where τ = (1 + √5) / 2~~ is the ~~[[golden ratio]] (also written φ)~~.

	~~==Orthogonal projections==~~
	~~The ''truncated dodecahedron'' has five special [[orthogonal projection]]s, centered,~~ on ~~a vertex, on two types~~ of ~~edges~~, and ~~two types of faces: hexagonal and pentagonal~~. The ~~last two correspond to~~ the ~~A<sub>2</sub>~~ and ~~H<sub>~~2~~</sub> [[Coxeter plane]]s~~.
	~~{\|class=wikitable~~
	~~\|+ Orthogonal projections~~
	\|-
	~~!Centered by~~
	~~!Vertex~~
	~~!Edge~~<br>~~3-10~~
	~~!Edge~~<br>~~10-10~~
	~~!Face~~<br>~~Triangle~~
	~~!Face~~<br>~~Decagon~~
	\|-
	~~!Image~~
	~~\|[[File:Dodecahedron_t01_v~~.~~png\|120px]]~~
	~~\|[[File:Dodecahedron_t01_e3x~~.~~png\|120px]]~~
	~~\|[[File~~:~~Dodecahedron_t01_exx~~.~~png\|120px]]~~
	~~\|[[File:Dodecahedron_t01_A2.png\|120px]]~~
	~~\|[[File:Dodecahedron_t01_H3.png\|120px]]~~
	~~\|- align=center~~
	~~!Projective~~<br>~~symmetry~~
	~~\|[2]~~
	~~\|[2]~~
	~~\|[2]~~
	~~\|[6]~~
	~~\|[10]~~
	\|}

	~~== Vertex arrangement==~~
	~~It shares its [[vertex arrangement]] with three [[nonconvex uniform polyhedra]]:~~
	~~{\|class="wikitable" width="400" style="vertical-align:top;text-align:center"~~
	~~\|[[Image:Truncated dodecahedron.png\|100px]]~~<br>~~Truncated dodecahedron~~
	~~\|[[Image~~:~~Great icosicosidodecahedron.png\|100px]]<br>~~[~~[Great icosicosidodecahedron]]~~
	~~\|[[Image~~:~~Great ditrigonal dodecicosidodecahedron~~.~~png\|100px]]<br>[[Great ditrigonal dodecicosidodecahedron]]~~
	~~\|[[Image:Great dodecicosahedron~~.~~png\|100px]]<br>[[Great dodecicosahedron]~~]
	\|}

	~~== Related polyhedra and tilings ==~~

	~~It is part~~ of a ~~truncation process between~~ a ~~dodecahedron and icosahedron:~~
	~~{{Icosahedral truncations}}~~

	~~This polyhedron is topologically related as~~ a part of ~~sequence~~ of ~~uniform [[Truncation (geometry)\|truncated]] polyhedra with [[vertex configuration]]s (3~~.~~2n.2n), and [n,3] [[Coxeter group]] symmetry.~~

	~~{{Truncated figure1 table}}~~

	~~==See also==~~
	*[[:Image:Truncateddodecahedron.gif\|Spinning truncated dodecahedron]]
	*[[Icosahedron]]
	*[[Icosidodecahedron]]
	*[[Truncated icosahedron]]

	~~==Notes==~~
	~~{{reflist}}~~

	~~==References==~~
	*{{The Geometrical Foundation of Natural Structure (book)}} (Section 3-9)
	*{{cite book\|author=Cromwell, P.\|year=1997\|title=Polyhedra\|location=United Kingdom\|publisher=Cambridge\|pages=79-86 ''Archimedean solids''\|isbn=0-521-55432-2}}

	~~==External links==~~
	*{{mathworld2 \| urlname = TruncatedDodecahedron\| title = Truncated dodecahedron \| urlname2 = ~~ArchimedeanSolid \| title2 = Archimedean solid}}~~
	*{{KlitzingPolytopes\|polyhedra.htm\|3D convex uniform polyhedra\|o3x5x - ~~tid}}~~
	*[http://www.~~dr-mikes-math-games-for-kids~~.~~com/polyhedral-nets~~.html?net=1e9V3YL5nW2MMkIcdn0TdMHHhXMiuoCQGqz2g3IjH7orIJ5iBy9LQ80CKQP1GAP9MmtklgzVBcF5ZfK9LsPLcjTfCVtbQWJrpIJTarRzJGitPNEnHrk3rNm5pr6Gzui1P5MD7RwSrFu6TKzjy5qQl5PYokM9mcFWcoPivzjQxlRGa1eVpVmZl5Uv2nXTaX5RSgc2N5B3daPbsAUEsCGxrnbgMLCKvMvztIjl44GGTstwl3pC589OwhVUTHvkTzg6b4dpshGHQn4ajtxQA8chKkqzW1wKBsKuMpbqE4oCXbIi2sfEgppN1tcDBWVOJUXQfPiEglU1jtQi7fUj5xDW2PpZtdwQDmwpC3Lk&name=Truncated+Dodecahedron#applet Editable printable net of a truncated dodecahedron with interactive 3D view]
	*[http://www.mathconsult.~~ch/showroom/unipoly/ The Uniform Polyhedra]~~
	*[http://www.~~georgehart~~.~~com/virtual-polyhedra/vp.html Virtual Reality Polyhedra] The Encyclopedia of Polyhedra~~

	~~{{Archimedean solids}}~~
	~~{{Polyhedron navigator}}~~

	~~[[Category:Uniform polyhedra]]~~
	~~[[Category:Archimedean solids]~~]

en>JRSpriggs: Undid revision 582610086 by 96.27.15.107 (talk) rvv

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