Uniform colorings edit A half symmetry [1+,4,5] = [5,5] coloring can be constructed with two colors of decagons. This coloring is called a truncated pentapentagonal tiling .
Symmetry edit There is only one subgroup of [5,5], [5,5]+ , removing all the mirrors. This symmetry can be doubled to 542 symmetry by adding a bisecting mirror.
Small index subgroups of [5,5] Type Reflective domains Rotational symmetry Index 1 2 Diagram Coxeter orbifold ) [5,5] = [5,5]+ =
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
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. See also edit
Wikimedia Commons has media related to Uniform tiling 4-10-10 .
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
truncated, order, pentagonal, tiling, truncated, pentagonal, tiling, poincaré, disk, model, hyperbolic, plane, type, hyperbolic, uniform, tiling, vertex, configuration, schläfli, symbol, wythoff, symbol, coxeter, diagram, symmetry, group, dual, order, tetrakis. Truncated pentagonal tiling Poincare disk model of the hyperbolic plane Type Hyperbolic uniform tiling Vertex configuration 4 10 10 Schlafli symbol t 5 4 Wythoff symbol 2 4 5 2 5 5 Coxeter diagram or Symmetry group 5 4 542 5 5 552 Dual Order 5 tetrakis square tiling Properties Vertex transitive In geometry the truncated order 4 pentagonal tiling is a uniform tiling of the hyperbolic plane It has Schlafli symbol of t0 1 5 4 Contents 1 Uniform colorings 2 Symmetry 3 Related polyhedra and tiling 4 References 5 See also 6 External linksUniform colorings editA half symmetry 1 4 5 5 5 coloring can be constructed with two colors of decagons This coloring is called a truncated pentapentagonal tiling nbsp Symmetry editThere is only one subgroup of 5 5 5 5 removing all the mirrors This symmetry can be doubled to 542 symmetry by adding a bisecting mirror Small index subgroups of 5 5 Type Reflective domains Rotational symmetry Index 1 2 Diagram nbsp nbsp Coxeter orbifold 5 5 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 552 5 5 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 552 Related polyhedra and tiling edit n42 symmetry mutation of truncated tilings 4 2n 2n vte Symmetry n42 n 4 Spherical Euclidean Compact hyperbolic Paracomp 242 2 4 342 3 4 442 4 4 542 5 4 642 6 4 742 7 4 842 8 4 42 4 Truncatedfigures nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp Config 4 4 4 4 6 6 4 8 8 4 10 10 4 12 12 4 14 14 4 16 16 4 n kisfigures nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp Config V4 4 4 V4 6 6 V4 8 8 V4 10 10 V4 12 12 V4 14 14 V4 16 16 V4 Uniform 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 5References 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 See also edit nbsp Wikimedia Commons has media related to Uniform tiling 4 10 10 Uniform tilings in hyperbolic plane List of regular polytopesExternal 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 Truncated order 4 pentagonal tiling amp oldid 1189601720 Symmetry, wikipedia, wiki , book, books, library,
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