Cantic order-4 hexagonal tiling

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
Cantic order-4 hexagonal tiling
Cantic order-4 hexagonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration 3.8.4.8
Schläfli symbol t0,1(4,4,3)
Wythoff symbol 4 4 | 3
Coxeter diagram File:CDel branch 01rd.pngFile:CDel split2-44.pngFile:CDel node 1.png
Symmetry group [(4,4,3)], (*443)
Dual Order-4-4-3 t01 dual tiling
Properties Vertex-transitive

In geometry, the cantic order-4 hexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t0,1{(4,4,3)} or h2{6,4}.

[edit | edit source]
Uniform (4,4,3) tilings
Symmetry: [(4,4,3)] (*443) [(4,4,3)]+
(443) 		[(4,4,3+)]
(3*22) 		[(4,1+,4,3)]
(*3232)
File:CDel branch 01rd.pngFile:CDel split2-44.pngFile:CDel node.png File:CDel branch 01rd.pngFile:CDel split2-44.pngFile:CDel node 1.png File:CDel branch.pngFile:CDel split2-44.pngFile:CDel node 1.png File:CDel branch 10ru.pngFile:CDel split2-44.pngFile:CDel node 1.png File:CDel branch 10ru.pngFile:CDel split2-44.pngFile:CDel node.png File:CDel branch 11.pngFile:CDel split2-44.pngFile:CDel node.png File:CDel branch 11.pngFile:CDel split2-44.pngFile:CDel node 1.png File:CDel branch hh.pngFile:CDel split2-44.pngFile:CDel node h.png File:CDel branch hh.pngFile:CDel split2-44.pngFile:CDel node.png File:CDel branch.pngFile:CDel split2-44.pngFile:CDel node h.png File:CDel branch 10ru.pngFile:CDel split2-44.pngFile:CDel node h.png
File:CDel node h.pngFile:CDel 6.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node.png File:CDel node h.pngFile:CDel 6.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node 1.png File:CDel node h0.pngFile:CDel 6.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node 1.png File:CDel node h.pngFile:CDel 6.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node 1.png File:CDel node h.pngFile:CDel 6.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node.png File:CDel node h0.pngFile:CDel 6.pngFile:CDel node 1.pngFile:CDel 4.pngFile:CDel node.png File:CDel node h0.pngFile:CDel 6.pngFile:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.png File:CDel node h0.pngFile:CDel 6.pngFile:CDel node h.pngFile:CDel 4.pngFile:CDel node h.png File:CDel node h0.pngFile:CDel 6.pngFile:CDel node h.pngFile:CDel 4.pngFile:CDel node.png File:CDel node h0.pngFile:CDel 6.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node h.png File:CDel node h1.pngFile:CDel 6.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node h1.png
File:Uniform tiling 443-t0.png File:Uniform tiling 443-t01.png File:Uniform tiling 443-t1.png File:Uniform tiling 443-t12.png File:Uniform tiling 443-t2.png File:Uniform tiling 443-t02.png File:Uniform tiling 443-t012.png File:Uniform tiling 443-snub1.png File:Uniform tiling 64-h1.png File:Uniform tiling 66-t2.png File:Uniform tiling verf 34664.png
h{6,4}
t0(4,4,3) 		h2{6,4}
t0,1(4,4,3) 		{4,6}1/2
t1(4,4,3) 		h2{6,4}
t1,2(4,4,3) 		h{6,4}
t2(4,4,3) 		r{6,4}1/2
t0,2(4,4,3) 		t{4,6}1/2
t0,1,2(4,4,3) 		s{4,6}1/2
s(4,4,3) 		hr{4,6}1/2
hr(4,3,4) 		h{4,6}1/2
h(4,3,4) 		q{4,6}
h1(4,3,4)
Uniform duals
File:Uniform tiling 66-t1.png File:Ord64 qreg rhombic til.png File:Order4 hexakis hexagonal til.png File:Uniform tiling 66-t0.png
V(3.4)4 V3.8.4.8 V(4.4)3 V3.8.4.8 V(3.4)4 V4.6.4.6 V6.8.8 V3.3.3.4.3.4 V(4.4.3)2 V66 V4.3.4.6.6

References

[edit | edit source]
  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value). (Chapter 19, The Hyperbolic Archimedean Tessellations)
  • Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).

See also

[edit | edit source]
Error creating thumbnail: File missing
Wikimedia Commons has media related to Uniform tiling 3-8-4-8.
[edit | edit source]


Stub icon

This hyperbolic geometry-related article is a stub. You can help Wikipedia by expanding it.

Retrieved from "http://70.231.62.181/index.php?title=Cantic_order-4_hexagonal_tiling&oldid=13258873"