七階四面體堆砌
在幾何學中,七階四面體堆砌是一種位於雙曲三維非緊空間的雙曲正堆砌,由正四面體組成,在施萊夫利符號中用{3,3,7}來表示,考克斯特-迪肯符號中以
七階四面體堆砌 | |
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類型 | 雙曲正堆砌 |
家族 | 堆砌 |
維度 | 三維雙曲空間 |
胞 | {3,3} ![]() |
面 | {3} ![]() |
顶点图 | ![]() ({3,7}) |
施萊夫利符號 | {3,3,7} |
考克斯特記號 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
對稱群 | [7,3,3] |
對偶多胞體 | 三階七邊形鑲嵌蜂巢體 |
特性 | 正 |
性質
由於正四面體不能堆滿三維空間,讓稜成為五個正四面體的公共稜之後,剩下的空間無法再放入一個正四面體,因此六階四面體堆砌就只能密鋪於雙曲空間[2],若再放入一個正四面體則無法存於雙曲緊湊空間,即圖形發散,無法收斂於無窮遠處。
相關多胞體與堆砌
七階四面體堆砌是一種由正四面體組成的堆砌,其他胞也由正四面體組成多胞體與堆砌或蜂巢體包含:
{3,3,p}多胞體 | |||||||||||
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空間 | S3 | H3 | |||||||||
構造 | 有限 | 仿緊 | 非緊 | ||||||||
施萊夫利符號 考克斯特符號 |
{3,3,3}![]() ![]() ![]() ![]() ![]() ![]() ![]() |
{3,3,4}![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
{3,3,5}![]() ![]() ![]() ![]() ![]() ![]() ![]() |
{3,3,6}![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
{3,3,7}![]() ![]() ![]() ![]() ![]() ![]() ![]() |
{3,3,8}![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
... {3,3,∞}![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | ||||
圖像 | ![]() |
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Vertex figure |
![]() {3,3} ![]() ![]() ![]() ![]() ![]() |
![]() {3,4} ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() {3,5} ![]() ![]() ![]() ![]() ![]() |
![]() {3,6} ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() {3,7} ![]() ![]() ![]() ![]() ![]() |
![]() {3,8} ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() {3,∞} ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
參見
參考文獻
- George Maxwell, Sphere Packings and Hyperbolic Reflection Groups, JOURNAL OF ALGEBRA 79,78-97 (1982) Archive.is的存檔,存档日期2013-06-30
- Hao Chen, Jean-Philippe Labbé, Lorentzian Coxeter groups and Boyd-Maxwell ball packings, (2013)页面存档备份,存于
- Humphreys, 1990, page 141, 6.9 List of hyperbolic Coxeter groups, figure 2 页面存档备份,存于
- The Beauty of Geometry: Twelve Essays (1999), Dover Publications, LCCN 99-35678, ISBN 0-486-40919-8 (Chapter 10, Regular Honeycombs in Hyperbolic Space 页面存档备份,存于)
- C. W. L. Garner, Regular Skew Polyhedra in Hyperbolic Three-Space Canad. J. Math. 19, 1179–1186, 1967. PDF 页面存档备份,存于
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