This tiling is topologically related as a part of sequence of cantellated polyhedra with vertex figure (3.4.n.4), and continues as tilings of the hyperbolic plane. These vertex-transitive figures have (*n32) reflectional symmetry.
*n32 symmetry mutation of dual expanded tilings: V3.4.n.4
John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations)
"Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. 1999. ISBN0-486-40919-8. LCCN 99035678.
rhombitriheptagonal, tiling, poincaré, disk, model, hyperbolic, planetype, hyperbolic, uniform, tilingvertex, configuration, 4schläfli, symbol, displaystyle, begin, bmatrix, bmatrix, wythoff, symbol, 2coxeter, diagram, orsymmetry, group, dual, deltoidal, trihe. Rhombitriheptagonal tilingPoincare disk model of the hyperbolic planeType Hyperbolic uniform tilingVertex configuration 3 4 7 4Schlafli symbol rr 7 3 or r 7 3 displaystyle r begin Bmatrix 7 3 end Bmatrix Wythoff symbol 3 7 2Coxeter diagram orSymmetry group 7 3 732 Dual Deltoidal triheptagonal tilingProperties Vertex transitiveIn geometry the rhombitriheptagonal tiling is a semiregular tiling of the hyperbolic plane At each vertex of the tiling there is one triangle and one heptagon alternating between two squares The tiling has Schlafli symbol rr 7 3 It can be seen as constructed as a rectified triheptagonal tiling r 7 3 as well as an expanded heptagonal tiling or expanded order 7 triangular tiling Contents 1 Dual tiling 2 Related polyhedra and tilings 2 1 Symmetry mutations 3 See also 4 References 5 External linksDual tiling EditThe dual tiling is called a deltoidal triheptagonal tiling and consists of congruent kites It is formed by overlaying an order 3 heptagonal tiling and an order 7 triangular tiling Related polyhedra and tilings EditFrom a Wythoff construction there are eight hyperbolic uniform tilings that can be based from the regular heptagonal tiling Drawing the tiles colored as red on the original faces yellow at the original vertices and blue along the original edges there are 8 forms Uniform heptagonal triangular tilings vteSymmetry 7 3 732 7 3 732 7 3 t 7 3 r 7 3 t 3 7 3 7 rr 7 3 tr 7 3 sr 7 3 Uniform duals V73 V3 14 14 V3 7 3 7 V6 6 7 V37 V3 4 7 4 V4 6 14 V3 3 3 3 7Symmetry mutations Edit This tiling is topologically related as a part of sequence of cantellated polyhedra with vertex figure 3 4 n 4 and continues as tilings of the hyperbolic plane These vertex transitive figures have n32 reflectional symmetry n32 symmetry mutation of dual expanded tilings V3 4 n 4 Symmetry n32 n 3 Spherical Euclid Compact hyperb Paraco 232 2 3 332 3 3 432 4 3 532 5 3 632 6 3 732 7 3 832 8 3 32 3 FigureConfig V3 4 2 4 V3 4 3 4 V3 4 4 4 V3 4 5 4 V3 4 6 4 V3 4 7 4 V3 4 8 4 V3 4 4See also Edit Wikimedia Commons has media related to Uniform tiling 3 4 7 4 Rhombitrihexagonal tiling Order 3 heptagonal tiling Tilings of regular polygons List of uniform tilings Kagome latticeReferences EditJohn H Conway Heidi Burgiel Chaim Goodman Strass 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 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 Rhombitriheptagonal tiling amp oldid 1169900898 Dual tiling, wikipedia, wiki, book, books, library,
