扭稜六邊形鑲嵌

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扭稜六邊形鑲嵌
扭稜六邊形鑲嵌
(點選檢視大圖)
類別 半正鑲嵌
頂點圖英语Vertex figure 3.3.3.3.6
頂點佈局 34.6
考克斯特符號英语Coxeter-Dynkin diagram CDel node h.pngCDel 6.pngCDel node h.pngCDel 3.pngCDel node h.png
施萊夫利符號 s{6,3}
威佐夫符號英语Wythoff symbol | 6 3 2
對稱群 p6, [6,3]+, (632)
對偶 花形五邊形鑲嵌
Rotation group p6, [6,3]+, (632)
特性 Vertex-transitive
Snub hexagonal tiling vertfig.png
3.3.3.3.6
(頂點圖)
Tiling Dual Semiregular V3-3-3-3-6 Floret Pentagonal.svg
花形五邊形鑲嵌
(對偶多面體)

幾何學中,扭稜六邊形鑲嵌歐幾里德平面六邊形鑲嵌的一種變形,是種平面鑲嵌,屬於半正鑲嵌圖的一種,它的每個頂點上皆有三角形六邊形。在施萊夫利符號中用s{6,3}來表示。

康威稱扭稜六邊形鑲嵌為snub hexatille,因為扭稜六邊形鑲嵌可由六邊形鑲嵌透過扭稜變換而構造出來。

相關半正鑲嵌[编辑]

正三角形镶嵌家族的半正镶嵌
对称性: [6,3], (*632) [6,3]+, (632) [1+,6,3], (*333) [6,3+], (3*3)
CDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node.png CDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.png CDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.png CDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png CDel node.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.png CDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.png CDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png CDel node h.pngCDel 6.pngCDel node h.pngCDel 3.pngCDel node h.png CDel node h.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node.png CDel node.pngCDel 6.pngCDel node h.pngCDel 3.pngCDel node h.png
Uniform tiling 63-t0.png Uniform tiling 63-t01.png Uniform tiling 63-t1.png Uniform tiling 63-t12.png Uniform tiling 63-t2.png Uniform tiling 63-t02.png Uniform tiling 63-t012.png Uniform tiling 63-snub.png Uniform tiling 333-t1.png Uniform tiling 63-h12.png
{6,3} t0,1{6,3} t1{6,3} t1,2{6,3} t2{6,3} t0,2{6,3} t0,1,2{6,3} s{6,3} h{6,3} h1,2{6,3}
半正对偶
CDel node f1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node.png CDel node f1.pngCDel 6.pngCDel node f1.pngCDel 3.pngCDel node.png CDel node.pngCDel 6.pngCDel node f1.pngCDel 3.pngCDel node.png CDel node.pngCDel 6.pngCDel node f1.pngCDel 3.pngCDel node f1.png CDel node.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node f1.png CDel node f1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node f1.png CDel node f1.pngCDel 6.pngCDel node f1.pngCDel 3.pngCDel node f1.png CDel node fh.pngCDel 6.pngCDel node fh.pngCDel 3.pngCDel node fh.png CDel node fh.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node.png CDel node.pngCDel 6.pngCDel node fh.pngCDel 3.pngCDel node fh.png
Uniform tiling 63-t2.png Tiling Dual Semiregular V3-12-12 Triakis Triangular.svg Rhombic star tiling.png Uniform tiling 63-t2.png Uniform tiling 63-t0.png Tiling Dual Semiregular V3-4-6-4 Deltoidal Trihexagonal.svg Tiling Dual Semiregular V4-6-12 Bisected Hexagonal.svg Tiling Dual Semiregular V3-3-3-3-6 Floret Pentagonal.svg Uniform tiling 63-t0.png
V6.6.6 V3.12.12 V3.6.3.6 V6.6.6 V3.3.3.3.3.3 V3.4.12.4 V.4.6.12 V3.3.3.3.6 V3.3.3.3.3.3

參考文獻[编辑]

  1. John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 [1]
  2. Richard Klitzing, 2D Euclidean tilings, s4s4s - snasquat - O10
  3. Grünbaum, Branko ; and Shephard, G. C. Tilings and Patterns. New York: W. H. Freeman. 1987. ISBN 0-7167-1193-1.  (Chapter 2.1: Regular and uniform tilings, p.58-65)
  4. Williams, Robert. The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. 1979. ISBN 0-486-23729-X.  p38
  5. MathWorldSemiregular tessellation 的资料,作者:埃里克·韦斯坦因