|
In geometry, an infinite skew polygon, also called a skew apeirogon has vertices that are not all colinear. Two primary forms have been studied by dimension, 2-dimensional zig-zag skew apeirogons vertices alternating between two parallel lines, and 3-dimensional helical skew apeirogons with vertices on the surface of a cylinder. In 2-dimensions they repeat as glide reflections,〔Coxeter, H. S. M. and Moser, W. O. J. (1980), p.54 5.2 The Petrie polygon〕 as screw axis in 3-dimensions. Regular skew apeirogon exist in the petrie polygons of the affine and hyperbolic Coxeter groups. They are constructed a a single operator as the composite of all the reflections of the Coxeter group.〔Kaleidoscopes: Selected Writings of H. S. M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 () (Definition: paper 13, Discrete groups generated by reflections, 1933, p. 161)〕 == Regular skew apeirogons in two dimensions== A regular skew zig-zag aperiogon has 2 *∞, D∞d Frieze group symmetry. The zig-zag regular skew apeirogons exists as Petrie polygons of the three regular tilings of the plane: , , and . These apeirogons have internal angles of 90°, 120°, and 60°, respectively, from the regular polygons within the tilings. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「skew apeirogon」の詳細全文を読む スポンサード リンク
|