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词条 Triapeirogonal tiling
释义

  1. Uniform colorings

  2. Related polyhedra and tiling

  3. See also

  4. References

  5. External links

{{Uniform hyperbolic tiles db|Uniform hyperbolic tiling stat table|Ui3_1}}

In geometry, the triapeirogonal tiling (or trigonal-horocyclic tiling) is a uniform tiling of the hyperbolic plane with a Schläfli symbol of r{∞,3}.

Uniform colorings

The half-symmetry form, {{CDD|labelinfin|branch_11|split2|node}}, has two colors of triangles:

Related polyhedra and tiling

This hyperbolic tiling is topologically related as a part of sequence of uniform quasiregular polyhedra with vertex configurations (3.n.3.n), and [n,3] Coxeter group symmetry.

{{Quasiregular3 table}}{{Order i-3 tiling table}}{{Order_i-3-3_tiling_table}}

See also

{{Commons category|Uniform tiling 3-i-3-i}}
  • List of uniform planar tilings
  • Tilings of regular polygons
  • Uniform tilings in hyperbolic plane

References

{{refbegin}}
  • 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

  • {{MathWorld | urlname= HyperbolicTiling | title = Hyperbolic tiling}}
  • {{MathWorld | urlname=PoincareHyperbolicDisk | title = Poincaré hyperbolic disk }}
  • http://bendwavy.org/klitzing/incmats/o3xinfino.htm
  • {{KlitzingPolytopes|../dimensions/hyperbolic.htm#2D-non-compact|2D|Non-Compact Tilings}} o3x∞o
{{Tessellation}}

5 : Apeirogonal tilings|Hyperbolic tilings|Isogonal tilings|Isotoxal tilings|Uniform tilings

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