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Cantic octagonal tiling

Summary

Cantic octagonal tiling
Cantic octagonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration 3.6.4.6
Schläfli symbol h2{8,3}
Wythoff symbol 4 3 | 3
Coxeter diagram =
Symmetry group [(4,3,3)], (*433)
Dual Order-4-3-3 t12 dual tiling
Properties Vertex-transitive

In geometry, the tritetratrigonal tiling or shieldotritetragonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t1,2(4,3,3). It can also be named as a cantic octagonal tiling, h2{8,3}.

Dual tiling edit

 

Related polyhedra and tiling edit

Uniform (4,3,3) tilings
  • v
  • t
  • e
Symmetry: [(4,3,3)], (*433) [(4,3,3)]+, (433)
                                       
                                               
               
h{8,3}
t0(4,3,3) 		r{3,8}1/2
t0,1(4,3,3) 		h{8,3}
t1(4,3,3) 		h2{8,3}
t1,2(4,3,3) 		{3,8}1/2
t2(4,3,3) 		h2{8,3}
t0,2(4,3,3) 		t{3,8}1/2
t0,1,2(4,3,3) 		s{3,8}1/2
s(4,3,3)
Uniform duals
               
V(3.4)3 V3.8.3.8 V(3.4)3 V3.6.4.6 V(3.3)4 V3.6.4.6 V6.6.8 V3.3.3.3.3.4
*n33 orbifold symmetries of cantic tilings: 3.6.n.6
  • v
  • t
  • e
Symmetry
*n32
[1+,2n,3]
= [(n,3,3)] 		Spherical Euclidean Compact Hyperbolic Paracompact
*233
[1+,4,3]
= [3,3] 		*333
[1+,6,3]
= [(3,3,3)] 		*433
[1+,8,3]
= [(4,3,3)] 		*533
[1+,10,3]
= [(5,3,3)] 		*633...
[1+,12,3]
= [(6,3,3)] 		*∞33
[1+,∞,3]
= [(∞,3,3)]
Coxeter
Schläfli 		      =    
h2{4,3} 		      =    
h2{6,3} 		      =     
h2{8,3} 		      =     
h2{10,3} 		      =     
h2{12,3} 		      =     
h2{∞,3}
Cantic
figure 		           
Vertex 3.6.2.6 3.6.3.6 3.6.4.6 3.6.5.6 3.6.6.6 3.6.∞.6
 
Domain 		           
Wythoff 2 3 | 3 3 3 | 3 4 3 | 3 5 3 | 3 6 3 | 3 ∞ 3 | 3
Dual
figure 		     
Face V3.6.2.6 V3.6.3.6 V3.6.4.6 V3.6.5.6 V3.6.6.6 V3.6.∞.6

References edit

  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations)
  • "Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. 1999. ISBN 0-486-40919-8. LCCN 99035678.

See also edit

 
Wikimedia Commons has media related to Uniform tiling 3-6-4-6.

External links edit