超無限面形
超無限面形又稱偽多面形(英語:)或雙曲無限面形(英語:)是一種雙曲鑲嵌,其相當於在雙曲面上構造一個無限面形,因而導致在拓樸結構上該多面形之面數比無限面形還多[1],因此它在施萊夫利符號中用{2,iπ/λ}表示。
雙曲無限面形 | |
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![]() 龐加萊圓盤模型 | |
類別 | 雙曲鑲嵌 |
頂點圖 | 2iπ/λ |
考克斯特符號 | ![]() ![]() ![]() ![]() ![]() |
施萊夫利符號 | {2,iπ/λ} |
威佐夫符號 | iπ/λ 2 2 2 | iπ/λ |
對稱群 | [iπ/λ,2], (*∞22) |
對偶 | 二階超無限邊形鑲嵌 |
旋轉對稱群 | [iπ/λ,2]+, (∞22) |
特性 | Vertex-transitive、 edge-transitive、 face-transitive、 發散 |
![]() 二階超無限邊形鑲嵌 (對偶多面體) | |
超無限面形,是一種位於雙曲平面上的正鑲嵌圖,可以視為多面形退化的類比,具有偽多邊形群(pseudogonal group)的對稱性,其考克斯特群為[iπ/λ,2],其可以視為無限面形在羅氏幾何中的類比。
相關鑲嵌
超無限面形是多面形家族{2, p}的算術極限——無限面形在雙曲空間的類比。
球面鑲嵌 | 歐式鑲嵌 仿緊空間 |
雙曲鑲嵌 非緊空間 | ||||||||||||
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1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | ... | ∞ | iπ/λ |
![]() ![]() ![]() {2,1} |
![]() ![]() ![]() ![]() ![]() {2,2} |
![]() ![]() ![]() ![]() ![]() {2,3} |
![]() ![]() ![]() ![]() ![]() {2,4} |
![]() ![]() ![]() ![]() ![]() {2,5} |
![]() ![]() ![]() ![]() ![]() {2,6} |
![]() ![]() ![]() ![]() ![]() {2,7} |
![]() ![]() ![]() ![]() ![]() {2,8} |
![]() ![]() ![]() ![]() ![]() {2,9} |
![]() ![]() ![]() ![]() ![]() ![]() {2,10} |
![]() ![]() ![]() ![]() ![]() ![]() {2,11} |
![]() ![]() ![]() ![]() ![]() ![]() {2,12} |
![]() ![]() ![]() ![]() ![]() {2,∞} |
![]() ![]() ![]() ![]() ![]() {2,iπ/λ} | |
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對稱群:[iπ/λ,2], (*∞22) | [iπ/λ,2]+, (∞22) | |||||||||
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{iπ/λ,2} | t{iπ/λ,2} | r{iπ/λ,2} | 2t{iπ/λ,2}=t{2,iπ/λ} | 2r{iπ/λ,2}={2,iπ/λ} | rr{iπ/λ,2} | tr{iπ/λ,2} | sr{iπ/λ,2} | |||
半正對偶 | ||||||||||
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V∞2 | V2.∞.∞ | V2.∞.2.∞ | V4.4.∞ | V2∞ | V2.4.∞.4 | V4.4.∞ | V3.3.2.3.∞ |
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