# 扭歪多邊形

## 三維的正扭歪多邊形

 扭歪四邊形 扭歪六邊形 扭歪八邊形 扭歪十邊形 扭歪十二邊形 {2}#{ } {3}#{ } {4}#{ } {5}#{ } {5/2}#{ } {5/3}#{ } {6}#{ } s{2,4} s{2,6} s{2,8} s{2,10} s{2,12}

 扭歪四邊形 扭歪六邊形 扭歪十邊形 二個{2}#{ } 三個{3}#{ } 二個{3}#{ } 二個{5/3}#{ }

### 三維空間的等角扭歪多邊形

{4,6|4} {6,4|4} {6,6|3}

{3}#{ }

{2}#{ }

{3}#{ }

## 四維的正扭歪多邊形

A4, [3,3,3] B4, [4,3,3] F4, [3,4,3] H4, [5,3,3]

{3,3,3}

{4,3,3}

{3,3,4}

{3,4,3}

{5,3,3}

{3,3,5}

## 參考文獻

1. Coxeter, H. S. M. Petrie Polygons. Regular Polytopes, 3rd ed. New York: Dover, 1973. (sec 2.6 Petrie Polygons pp. 24–25, and Chapter 12, pp. 213–235, The generalized Petrie polygon )
2. Coxeter, H. S. M. & Moser, W. O. J. Generators and Relations for Discrete Groups. New York: Springer-Verlag. 1980. ISBN 0-387-09212-9. (1st ed, 1957) 5.2 The Petrie polygon {p,q}.
3. John Milnor: On the total curvature of knots, Ann. Math. 52 (1950) 248–257.
4. J.M. Sullivan: Curves of finite total curvature, ArXiv:math.0606007v2
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