Order-3 truncated heptagonal tiling

Order-3 truncated heptagonal tiling
Poincaré_disk_model
Type	Hyperbolic semiregular tiling
Vertex figure	3.14.14
Schläfli symbol	t{7,3}
Wythoff symbol	2 3 | 7
Coxeter-Dynkin
Symmetry	[7,3]
Dual	Order-7 triakis triangular tiling
Properties	Vertex-transitive

In geometry, the Truncated order-3 heptagonal tiling is a semiregular tiling of the hyperbolic plane. There is one triangle and two tetrakaidecagons on each vertex. It has Schläfli symbol of t_0,1{7,3}.

Dual tiling

The dual tiling is called an order-7 triakis triangular tiling, seen as an order-7 triangular tiling with each triangle divided into three by a center point.

Related polyhedra and tilings

This hyperbolic tiling is topologically related as a part of sequence of uniform truncated polyhedra with vertex configurations (3.2n.2n), and [n,3] Coxeter group symmetry.

3.4.4	3.6.6	3.8.8	3.10.10
3.12.12	3.14.14	3.16.16	3.∞.∞

See also

• Truncated hexagonal tiling
• Order-3 heptagonal tiling
• Tilings of regular polygons
• List of uniform 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)
• The Beauty of Geometry: Twelve Essays (1999), Dover Publications, LCCN 99-35678, ISBN 0-486-40919-8 (Chapter 10: Regular honeycombs in hyperbolic space)

External links

• Weisstein, Eric W., "Hyperbolic tiling" from MathWorld.
• Weisstein, Eric W., "Poincaré hyperbolic disk" from MathWorld.
• Hyperbolic and Spherical Tiling Gallery
• KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
• Hyperbolic Planar Tessellations, Don Hatch

This geometry-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Geometry stubs Tiling Wikimedia Foundation. 2010. Игры ⚽ Нужно решить контрольную? Tikkakoski Hans Dorjee Look at other dictionaries: Order-7 truncated triangular tiling — Poincaré disk model Type Hyperbolic semiregular tiling Vertex figure 7.6.6 Schläfli symbol t{3,7} …   Wikipedia Order-3 heptagonal tiling — Poincaré disk model of the hyperbolic plane Type Regular hyperbolic tiling Vertex figure 7.7.7 Schläfli symbol(s) …   Wikipedia Bisected hexagonal tiling — Type Dual semiregular tiling Faces 30 60 90 triangle Face configuration V4.6.12 …   Wikipedia List of mathematics articles (O) — NOTOC O O minimal theory O Nan group O(n) Obelus Oberwolfach Prize Object of the mind Object theory Oblate spheroid Oblate spheroidal coordinates Oblique projection Oblique reflection Observability Observability Gramian Observable subgroup… …   Wikipedia Conway polyhedron notation — This example chart shows how 11 new forms can be derived from the cube using 3 operations. The new polyhedra are shown as maps on the surface of the cube so the topological changes are more apparent. Vertices are marked in all forms with circles …   Wikipedia Symbole de Wythoff — Exemple des triangles de construction de Wythoff avec les 7 points générateurs. Les droites des miroirs actifs sont colorés en rouge, jaune et bleu avec les 3 noeuds qui leur sont opposés associés par le symbole de Wythoff. En géométrie, un… …   Wikipédia en Français Symbole de wythoff — Exemple des triangles de construction de Wythoff avec les 7 points générateurs. Les droites des miroirs actifs sont colorés en rouge, jaune et bleu avec les 3 noeuds qui leur sont opposés associés par le symbole de Wythoff. En géométrie, un… …   Wikipédia en Français Octahedron — For the album by The Mars Volta, see Octahedron (album). Regular Octahedron (Click here for rotating model) Type Platonic solid Elements F = 8, E = 12 V = 6 (χ = 2) Faces by sides …   Wikipedia List of mathematics articles (H) — NOTOC H H cobordism H derivative H index H infinity methods in control theory H relation H space H theorem H tree Haag s theorem Haagerup property Haaland equation Haar measure Haar wavelet Haboush s theorem Hackenbush Hadamard code Hadamard… …   Wikipedia List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”