Symmetry edit A half symmetry [1+ ,4,5] = [5,5] construction exists, which can be seen as two colors of pentagons. This coloring can be called a rhombipentapentagonal tiling .
Dual tiling edit Related polyhedra and tiling edit Uniform pentagonal/square tilings Symmetry: [5,4], (*542) [5,4]+ , (542) [5+ ,4], (5*2) [5,4,1+ ], (*552) {5,4} t{5,4} r{5,4} 2t{5,4}=t{4,5} 2r{5,4}={4,5} rr{5,4} tr{5,4} sr{5,4} s{5,4} h{4,5} Uniform duals V54 V4.10.10 V4.5.4.5 V5.8.8 V45 V4.4.5.4 V4.8.10 V3.3.4.3.5 V3.3.5.3.5 V55
Uniform pentapentagonal tilings Symmetry: [5,5], (*552) [5,5]+ , (552) Order-5 pentagonal tiling {5,5} Truncated order-5 pentagonal tiling t{5,5} Order-4 pentagonal tiling r{5,5} Truncated order-5 pentagonal tiling 2t{5,5} = t{5,5} Order-5 pentagonal tiling 2r{5,5} = {5,5} Tetrapentagonal tiling rr{5,5} Truncated order-4 pentagonal tiling tr{5,5} Snub pentapentagonal tiling sr{5,5} Uniform duals Order-5 pentagonal tiling V5.5.5.5.5 V5.10.10 Order-5 square tiling V5.5.5.5 V5.10.10 Order-5 pentagonal tiling V5.5.5.5.5 V4.5.4.5 V4.10.10 V3.3.5.3.5
*5n 2 symmetry mutations of quasiregular tilings: (5.n)2 Symmetryn 2 Spherical Hyperbolic Paracompact Noncompact *352 *452 *552 *652 *752 *852 *∞52 n i,5] Figures Config. (5.3)2 (5.4)2 (5.5)2 (5.6)2 (5.7)2 (5.8)2 (5.∞)2 (5.n i)2 Rhombic Config. V(5.3)2 V(5.4)2 V(5.5)2 V(5.6)2 V(5.7)2 V(5.8)2 V(5.∞)2 V(5.∞)2
See also edit
Wikimedia Commons has media related to Uniform tiling 4-5-4-5 .
References edit John H. Conway , Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations)"Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays . Dover Publications. 1999. ISBN 0-486-40919-8 LCCN 99035678. External links edit Weisstein, Eric W. "Hyperbolic tiling". MathWorld Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld Hyperbolic and Spherical Tiling Gallery KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings Hyperbolic Planar Tessellations, Don Hatch
tetrapentagonal, tiling, poincaré, disk, model, hyperbolic, plane, type, hyperbolic, uniform, tiling, vertex, configuration, schläfli, symbol, displaystyle, begin, bmatrix, bmatrix, displaystyle, begin, bmatrix, bmatrix, wythoff, symbol, coxeter, diagram, symm. Tetrapentagonal tiling Poincare disk model of the hyperbolic plane Type Hyperbolic uniform tiling Vertex configuration 4 5 2 Schlafli symbol r 5 4 or 5 4 displaystyle begin Bmatrix 5 4 end Bmatrix rr 5 5 or r 5 5 displaystyle r begin Bmatrix 5 5 end Bmatrix Wythoff symbol 2 5 45 5 2 Coxeter diagram or or Symmetry group 5 4 542 5 5 552 Dual Order 5 4 rhombille tiling Properties Vertex transitive edge transitive In geometry the tetrapentagonal tiling is a uniform tiling of the hyperbolic plane It has Schlafli symbol of t1 4 5 or r 4 5 Contents 1 Symmetry 2 Dual tiling 3 Related polyhedra and tiling 4 See also 5 References 6 External linksSymmetry editA half symmetry 1 4 5 5 5 construction exists which can be seen as two colors of pentagons This coloring can be called a rhombipentapentagonal tiling nbsp Dual tiling editThe dual tiling is made of rhombic faces and has a face configuration V4 5 4 5 nbsp Related polyhedra and tiling editUniform pentagonal square tilings vte Symmetry 5 4 542 5 4 542 5 4 5 2 5 4 1 552 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 5 4 t 5 4 r 5 4 2t 5 4 t 4 5 2r 5 4 4 5 rr 5 4 tr 5 4 sr 5 4 s 5 4 h 4 5 Uniform duals nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp V54 V4 10 10 V4 5 4 5 V5 8 8 V45 V4 4 5 4 V4 8 10 V3 3 4 3 5 V3 3 5 3 5 V55 Uniform pentapentagonal tilings vte Symmetry 5 5 552 5 5 552 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp Order 5 pentagonal tiling 5 5 Truncated order 5 pentagonal tiling t 5 5 Order 4 pentagonal tiling r 5 5 Truncated order 5 pentagonal tiling 2t 5 5 t 5 5 Order 5 pentagonal tiling 2r 5 5 5 5 Tetrapentagonal tiling rr 5 5 Truncated order 4 pentagonal tiling tr 5 5 Snub pentapentagonal tiling sr 5 5 Uniform duals nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp Order 5 pentagonal tiling V5 5 5 5 5 V5 10 10 Order 5 square tiling V5 5 5 5 V5 10 10 Order 5 pentagonal tiling V5 5 5 5 5 V4 5 4 5 V4 10 10 V3 3 5 3 5 n42 symmetry mutations of quasiregular tilings 4 n 2 vte Symmetry 4n2 n 4 Spherical Euclidean Compact hyperbolic Paracompact Noncompact 342 3 4 442 4 4 542 5 4 642 6 4 742 7 4 842 8 4 42 4 ni 4 Figures nbsp nbsp nbsp nbsp nbsp nbsp nbsp Config 4 3 2 4 4 2 4 5 2 4 6 2 4 7 2 4 8 2 4 2 4 ni 2 5n2 symmetry mutations of quasiregular tilings 5 n 2 vte Symmetry 5n2 n 5 Spherical Hyperbolic Paracompact Noncompact 352 3 5 452 4 5 552 5 5 652 6 5 752 7 5 852 8 5 52 5 ni 5 Figures nbsp nbsp nbsp nbsp nbsp nbsp nbsp Config 5 3 2 5 4 2 5 5 2 5 6 2 5 7 2 5 8 2 5 2 5 ni 2 Rhombicfigures nbsp nbsp nbsp nbsp Config V 5 3 2 V 5 4 2 V 5 5 2 V 5 6 2 V 5 7 2 V 5 8 2 V 5 2 V 5 2See also edit nbsp Wikimedia Commons has media related to Uniform tiling 4 5 4 5 Uniform tilings in hyperbolic plane List of regular polytopesReferences editJohn H Conway Heidi Burgiel Chaim Goodman Strauss The Symmetries of Things 2008 ISBN 978 1 56881 220 5 Chapter 19 The Hyperbolic Archimedean Tessellations Chapter 10 Regular honeycombs in hyperbolic space The Beauty of Geometry Twelve Essays Dover Publications 1999 ISBN 0 486 40919 8 LCCN 99035678 External links editWeisstein Eric W Hyperbolic tiling MathWorld Weisstein Eric W Poincare hyperbolic disk MathWorld Hyperbolic and Spherical Tiling Gallery KaleidoTile 3 Educational software to create spherical planar and hyperbolic tilings Hyperbolic Planar Tessellations Don Hatch nbsp This hyperbolic geometry related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Tetrapentagonal tiling amp oldid 1189602018, wikipedia, wiki , book, books, library,
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