| 释义 |
- Constructions
- Symmetry
- Related polyhedra and tiling
- References
- See also
- External links
{{Uniform hyperbolic tiles db|Uniform hyperbolic tiling stat table|U74_01}}In geometry, the truncated order-4 heptagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t{7,4}. Constructions There are two uniform constructions of this tiling, first by the [7,4] kaleidoscope, and second by removing the last mirror, [7,4,1+], gives [7,7], (*772). Two uniform constructions of 4.7.4.7| Name | Tetraheptagonal | Truncated heptahexagonal |
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| Image |
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| Symmetry | (*742)
{{CDD>node_c1|7|node_c2|4|node_c3}} | +]
(*772)
{{CDD>node_c1|split1-77|nodeab_c2}} = {{CDD|node_c1|7|node_c2|4|node_h0}} |
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| Symbol | t{7,4} | tr{7,7} |
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| Coxeter diagram | node_1|7|node_1|4|node}} | node_1|7|node_1|7|node_1}} |
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Symmetry There is only one simple subgroup [7,7]+, index 2, removing all the mirrors. This symmetry can be doubled to 742 symmetry by adding a bisecting mirror. Small index subgroups of [7,7]| Type | Reflectional | Rotational |
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| Index | 1 | 2 |
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| Diagram |
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Coxeter
(orbifold) | node_c1|7|node_c1|7|node_c1}}
(*772) | + = {{CDD>node_h2|7|node_h2|7|node_h2}}
(772) |
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Related polyhedra and tiling {{Truncated_figure3_table}}{{Order 7-4 tiling table}}{{Order 7-7 tiling table}}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}}
See also{{Commonscat|Uniform tiling 4-14-14}}- Uniform tilings in hyperbolic plane
- List of regular polytopes
External links - {{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}}{{geometry-stub}} 6 : Heptagonal tilings|Hyperbolic tilings|Isogonal tilings|Order-4 tilings|Truncated tilings|Uniform tilings |