Cantic order-4 hexagonal tiling
Cantic order-4 hexagonal tiling
Poincaré disk model of the hyperbolic plane
TypeHyperbolic uniform tiling
Vertex configuration3.8.4.8
Schläfli symbolt0,1(4,4,3)
Wythoff symbol4 4 | 3
Coxeter diagram
Symmetry group[(4,4,3)], (*443)
DualOrder-4-4-3 t01 dual tiling
PropertiesVertex-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}.

Uniform (4,4,3) tilings
Symmetry: [(4,4,3)] (*443) [(4,4,3)]+
(443)		 [(4,4,3+)]
(3*22)		 [(4,1+,4,3)]
(*3232)
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
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

  • 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

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