子群B（B_4）和W（B_3）*W（A_1）下W（F_4）多胞形及其对偶多胞形和分支的构造
Quaterionic Construction of the W(F_4) Polytopes with Their Dual Polytopes and Branching under the Subgroups B(B_4) and W(B_3)*W(A_1)
摘要：
4-本文构造了二维$F_{4} $多面体及其对偶多面体作为Coxeter-Weyl群$W(F_{4})$的轨道，其中多面体的群元和顶点用四元数表示.给出了任意\textbf{$W(F_{4})$}轨道在Coxeter群$W(B_{4} $和$W(B_{3}) \times W(A_{1})$下的分支.强调了群论技术的作用和四元数的使用
英文摘要：
4-dimensional $F_{4} $ polytopes and their dual polytopes have been constructed as the orbits of the Coxeter-Weyl group $W(F_{4})$ where the group elements and the vertices of the polytopes are represented by quaternions. Branchings of an arbitrary \textbf{$W(F_{4})$} orbit under the Coxeter groups $W(B_{4} $ and $W(B_{3}) \times W(A_{1})$ have been presented. The role of group theoretical technique and the use of quaternions have been emphasized
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