| 释义 |
- Uniform constructions
- Symmetry
- Related polyhedra and tiling
- See also
- References
- External links
{{Uniform hyperbolic tiles db|Uniform hyperbolic tiling stat table|Ui4_1}}In geometry, the tetraapeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of r{∞,4}. Uniform constructionsThere are 3 lower symmetry uniform construction, one with two colors of apeirogons, one with two colors of squares, and one with two colors of each: | Symmetry | (*∞42)
[∞,4] | (*∞33)
[1+,∞,4] = [(∞,4,4)] | (*∞∞2)
[∞,4,1+] = [∞,∞] | (*∞2∞2)
[1+,∞,4,1+] |
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| Coxeter | node|infin|node_1|4|node}} | node_h0|infin|node_1|4|node}} = {{CDD|labelinfin|branch_11|split2-44|node}} | node|infin|node_1|4|node_h0}} = {{CDD|node|split1-ii|nodes_11}} | node_h0|infin|node_1|4|node_h0}} = {{CDD|labelinfin|branch_11|2a2b-cross|branch_11 | labelinfin} |
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| Schläfli | r{∞,4} | 1|2}} | 1|2}}=rr{∞,∞} | 1|4}} |
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| Coloring |
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| Dual |
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SymmetryThe dual to this tiling represents the fundamental domains of *∞2∞2 symmetry group. The symmetry can be doubled by adding mirrors on either diagonal of the rhombic domains, creating *∞∞2 and *∞44 symmetry. Related polyhedra and tiling{{Quasiregular4 table}}{{Order i-4 tiling table}}{{Order i-i tiling table}}See also{{Commons category|Uniform tiling 4-i-4-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}}
{{Tessellation}} 5 : Apeirogonal tilings|Hyperbolic tilings|Isogonal tilings|Isotoxal tilings|Uniform tilings |