التفاصيل البيبلوغرافية
| العنوان: |
The Symmetry Group of the Grand Antiprism. |
| المؤلفون: |
Monson, Barry |
| المصدر: |
Symmetry (20738994); Aug2024, Vol. 16 Issue 8, p1071, 13p |
| مصطلحات موضوعية: |
COXETER groups, SYMMETRY groups, QUATERNIONS, GEOMETRY |
| مستخلص: |
The grand antiprism A is an outlier among the uniform 4-polytopes, since it is not obtainable from Wythoff's construction. Its symmetry group G (A) has been incorrectly described as [ [ 10 , 2 + , 10 ] ] or even as an 'ionic diminished Coxeter group'. In fact, G (A) is another group of order 400, namely the group ± [ D 10 × D 10 ] · 2 , in the notation of Conway and Smith. We explain all this and so correct a persistent error in the literature. This fresh look at the beautiful geometry of the polytope A is also a fine opportunity to introduce the reader to the elegance of Wythoff's construction and to the less familiar use of quaternions to classify the finite 4-dimensional isometry groups. [ABSTRACT FROM AUTHOR] |
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