Snub heptaheptagonal tiling

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Snub heptaheptagonal tiling
Snub heptaheptagonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration 3.3.7.3.7
Schläfli symbol sr{7,7} or
Wythoff symbol | 7 7 2
Coxeter diagram CDel node h.pngCDel 7.pngCDel node h.pngCDel 7.pngCDel node h.png
CDel node h.pngCDel 7.pngCDel node h.pngCDel 4.pngCDel node.png
Symmetry group [7,7]+, (772)
[7+,4], (7*2)
Dual
Properties Vertex-transitive

In geometry, the snub heptaheptagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of sr{7,7}, constructed from two regular heptagons and three equilateral triangles around every vertex.

Images[]

Drawn in chiral pairs, with edges missing between black triangles:

H2 snub 277a.pngH2 snub 277b.png

Symmetry[]

A double symmetry coloring can be constructed from [7,4] symmetry with only one color heptagon.

Uniform tiling 74-h01.png

Related tilings[]

Uniform heptaheptagonal tilings
  • v
Symmetry: [7,7], (*772) [7,7]+, (772)
CDel node 1.pngCDel 7.pngCDel node.pngCDel 7.pngCDel node.png = CDel nodes 10ru.pngCDel split2-77.pngCDel node.png
= CDel node h1.pngCDel 4.pngCDel node.pngCDel 7.pngCDel node.png 		CDel node 1.pngCDel 7.pngCDel node 1.pngCDel 7.pngCDel node.png = CDel nodes 10ru.pngCDel split2-77.pngCDel node 1.png
= CDel node h1.pngCDel 4.pngCDel node.pngCDel 7.pngCDel node 1.png 		CDel node.pngCDel 7.pngCDel node 1.pngCDel 7.pngCDel node.png = CDel nodes.pngCDel split2-77.pngCDel node 1.png
= CDel node h0.pngCDel 4.pngCDel node.pngCDel 7.pngCDel node 1.png 		CDel node.pngCDel 7.pngCDel node 1.pngCDel 7.pngCDel node 1.png = CDel nodes 01rd.pngCDel split2-77.pngCDel node 1.png
= CDel node h1.pngCDel 4.pngCDel node.pngCDel 7.pngCDel node 1.png 		CDel node.pngCDel 7.pngCDel node.pngCDel 7.pngCDel node 1.png = CDel nodes 01rd.pngCDel split2-77.pngCDel node.png
= CDel node h1.pngCDel 4.pngCDel node.pngCDel 7.pngCDel node.png 		CDel node 1.pngCDel 7.pngCDel node.pngCDel 7.pngCDel node 1.png = CDel nodes 11.pngCDel split2-77.pngCDel node.png
= CDel node h0.pngCDel 4.pngCDel node 1.pngCDel 7.pngCDel node.png 		CDel node 1.pngCDel 7.pngCDel node 1.pngCDel 7.pngCDel node 1.png =CDel nodes 11.pngCDel split2-77.pngCDel node 1.png
= CDel node h0.pngCDel 4.pngCDel node 1.pngCDel 7.pngCDel node 1.png 		CDel node h.pngCDel 7.pngCDel node h.pngCDel 7.pngCDel node h.png =CDel nodes hh.pngCDel split2-77.pngCDel node h.png
= CDel node h0.pngCDel 4.pngCDel node h.pngCDel 7.pngCDel node h.png
Uniform tiling 77-t0.png Uniform tiling 77-t01.png Uniform tiling 77-t1.png Uniform tiling 77-t12.png Uniform tiling 77-t2.png Uniform tiling 77-t02.png Uniform tiling 77-t012.png Uniform tiling 77-snub.png
{7,7} t{7,7}
 r{7,7} 2t{7,7}=t{7,7} 2r{7,7}={7,7} rr{7,7} tr{7,7} sr{7,7}
Uniform duals
CDel node f1.pngCDel 7.pngCDel node.pngCDel 7.pngCDel node.png CDel node f1.pngCDel 7.pngCDel node f1.pngCDel 7.pngCDel node.png CDel node.pngCDel 7.pngCDel node f1.pngCDel 7.pngCDel node.png CDel node.pngCDel 7.pngCDel node f1.pngCDel 7.pngCDel node f1.png CDel node.pngCDel 7.pngCDel node.pngCDel 7.pngCDel node f1.png CDel node f1.pngCDel 7.pngCDel node.pngCDel 7.pngCDel node f1.png CDel node f1.pngCDel 7.pngCDel node f1.pngCDel 7.pngCDel node f1.png CDel node fh.pngCDel 7.pngCDel node fh.pngCDel 7.pngCDel node fh.png
Uniform tiling 77-t2.png Order7 heptakis heptagonal til.png Uniform tiling 74-t2.png Order7 heptakis heptagonal til.png Uniform tiling 77-t0.png Ord74 qreg rhombic til.png Hyperbolic domains 772.png
V77 V7.14.14 V7.7.7.7 V7.14.14 V77 V4.7.4.7 V4.14.14 V3.3.7.3.7
Uniform heptagonal/square tilings
  • v
Symmetry: [7,4], (*742) [7,4]+, (742) [7+,4], (7*2) [7,4,1+], (*772)
CDel node 1.pngCDel 7.pngCDel node.pngCDel 4.pngCDel node.png CDel node 1.pngCDel 7.pngCDel node 1.pngCDel 4.pngCDel node.png CDel node.pngCDel 7.pngCDel node 1.pngCDel 4.pngCDel node.png CDel node.pngCDel 7.pngCDel node 1.pngCDel 4.pngCDel node 1.png CDel node.pngCDel 7.pngCDel node.pngCDel 4.pngCDel node 1.png CDel node 1.pngCDel 7.pngCDel node.pngCDel 4.pngCDel node 1.png CDel node 1.pngCDel 7.pngCDel node 1.pngCDel 4.pngCDel node 1.png CDel node h.pngCDel 7.pngCDel node h.pngCDel 4.pngCDel node h.png CDel node h.pngCDel 7.pngCDel node h.pngCDel 4.pngCDel node.png CDel node.pngCDel 7.pngCDel node.pngCDel 4.pngCDel node h.png
Uniform tiling 74-t0.png Uniform tiling 74-t01.png Uniform tiling 74-t1.png Uniform tiling 74-t12.png Uniform tiling 74-t2.png Uniform tiling 74-t02.png Uniform tiling 74-t012.png Uniform tiling 74-snub.png Uniform tiling 74-h01.png Uniform tiling 77-t0.png
{7,4} t{7,4} r{7,4} 2t{7,4}=t{4,7} 2r{7,4}={4,7} rr{7,4} tr{7,4} sr{7,4} s{7,4} h{4,7}
Uniform duals
CDel node f1.pngCDel 7.pngCDel node.pngCDel 4.pngCDel node.png CDel node f1.pngCDel 7.pngCDel node f1.pngCDel 4.pngCDel node.png CDel node.pngCDel 7.pngCDel node f1.pngCDel 4.pngCDel node.png CDel node.pngCDel 7.pngCDel node f1.pngCDel 4.pngCDel node f1.png CDel node.pngCDel 7.pngCDel node.pngCDel 4.pngCDel node f1.png CDel node f1.pngCDel 7.pngCDel node.pngCDel 4.pngCDel node f1.png CDel node f1.pngCDel 7.pngCDel node f1.pngCDel 4.pngCDel node f1.png CDel node fh.pngCDel 7.pngCDel node fh.pngCDel 4.pngCDel node fh.png CDel node fh.pngCDel 7.pngCDel node fh.pngCDel 4.pngCDel node.png CDel node.pngCDel 7.pngCDel node.pngCDel 4.pngCDel node fh.png
Uniform tiling 74-t2.png Hyperbolic domains 772.png Ord74 qreg rhombic til.png Order4 heptakis heptagonal til.png Uniform tiling 74-t0.png Deltoidal tetraheptagonal til.png Hyperbolic domains 742.png Uniform tiling 77-t2.png
V74 V4.14.14 V4.7.4.7 V7.8.8 V47 V4.4.7.4 V4.8.14 V3.3.4.3.7 V3.3.7.3.7 V77
4n2 symmetry mutations of snub tilings: 3.3.n.3.n
Symmetry
4n2 		Spherical Euclidean Compact hyperbolic Paracompact
222 322 442 552 662 772 882 ∞∞2
Snub
figures 		Digonal antiprism.png Pseudoicosahedron-3.png Uniform tiling 44-snub.png Uniform tiling 552-snub.png Uniform tiling 66-snub.png Uniform tiling 77-snub.png Uniform tiling 88-snub.png Uniform tiling ii2-snub.png
Config. 3.3.2.3.2 3.3.3.3.3 3.3.4.3.4 3.3.5.3.5 3.3.6.3.6 3.3.7.3.7 3.3.8.3.8 3.3.∞.3.∞
Gyro
figures 		Digonal trapezohedron.png Pyritohedron.png Tiling Dual Semiregular V3-3-4-3-4 Cairo Pentagonal.svg Infinitely-infinite-order floret pentagonal tiling.png
Config. V3.3.2.3.2 V3.3.3.3.3 V3.3.4.3.4 V3.3.5.3.5 V3.3.6.3.6 V3.3.7.3.7 V3.3.8.3.8 V3.3.∞.3.∞

See also[]

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)
  • "Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. 1999. ISBN 0-486-40919-8. LCCN 99035678.

External links[]

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