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摘要
En 中文
A reflection in Euclidean n-dimensional space is a
particular type of congruent transformation which is of period two and
leaves a prime (i.e., hyperplane) invariant. Groups generated by a number of
these reflections have been extensively studied [5, pp. 187-212]. They are
of interest since, with very few exceptions, the symmetry groups of uniform
polytopes are of this type. Coxeter has also shown [4] that it is possible,
by Wythoff's construction, to derive a number of uniform polytopes from any
group generated by reflections. His discussion of this construction is
elegantly illustrated by the use of a graphical notation [4, p. 328; 5, p.
84] whereby the properties of the polytopes can be read off from a simple
graph of nodes, branches, and rings.
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