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词条 Snub hexaoctagonal tiling
释义

  1. Images

  2. Related polyhedra and tilings

  3. See also

  4. References

  5. External links

{{Uniform hyperbolic tiles db|Uniform hyperbolic tiling stat table|U86_s}}

In geometry, the snub hexaoctagonal tiling is a semiregular tiling of the hyperbolic plane. There are three triangles, one hexagon, and one octagon on each vertex. It has Schläfli symbol of sr{8,6}.

Images

Drawn in chiral pairs, with edges missing between black triangles:

Related polyhedra and tilings

From a Wythoff construction there are fourteen hyperbolic uniform tilings that can be based from the regular order-6 octagonal tiling.

Drawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, there are 7 forms with full [8,6] symmetry, and 7 with subsymmetry.

{{Order 8-6 tiling table}}

See also

  • Tilings of regular polygons
  • List of uniform planar tilings

References

  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, {{isbn|978-1-56881-220-5}} (Chapter 19, The Hyperbolic Archimedean Tessellations)
  • {{Cite book|title=The Beauty of Geometry: Twelve Essays|year=1999|publisher=Dover Publications|lccn=99035678|isbn=0-486-40919-8|chapter=Chapter 10: Regular honeycombs in hyperbolic space}}

External links

{{Commonscat|Uniform tiling 3-3-6-3-8}}
  • {{MathWorld | urlname= HyperbolicTiling | title = Hyperbolic tiling}}
  • {{MathWorld | urlname=PoincareHyperbolicDisk | title = Poincaré hyperbolic disk }}
  • Hyperbolic and Spherical Tiling Gallery
  • KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
  • Hyperbolic Planar Tessellations, Don Hatch
{{Tessellation}}

5 : Chiral figures|Hyperbolic tilings|Isogonal tilings|Semiregular tilings|Snub tilings

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