Order-8 triangular tiling: Difference between revisions

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{{Short description|Concept in geometry}}

{{Uniform hyperbolic tiles db|Reg hyperbolic tiling stat table|U83_2}}

In [[geometry]], the '''order-8 triangular tiling''' is a [[regular hyperbolic tiling|regular tiling]] of the [[Hyperbolic geometry|hyperbolic plane]]. It is represented by [[Schläfli symbol]] of ''{3,8}'', having eight regular [[triangle]]s around each vertex.

== Uniform colorings ==

The half symmetry [1⁺,8,3] = [(4,3,3)] can be shown with alternating two colors of triangles:

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{{Triangular regular tiling}}

From a [[Wythoff construction]] there are ten hyperbolic [[Uniform tilings in hyperbolic plane|uniform tilings]] that can be based from the regular octagonal and order-8 triangular tilings.

Drawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, there are 10 forms.

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{{reflist}}

{{refbegin}}

* [[John Horton Conway|John H. Conway]], Heidi Burgiel, Chaim Goodman-StrassStrauss, ''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}}

{{refend}}

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[[Category:Isogonal tilings]]

[[Category:Isohedral tilings]]

[[Category:Order-8 tilings]]

[[Category:Regular tilings]]

[[Category:Triangular tilings]]