Construction of Mercedes–Benz Frame in $${\mathbb {R}}^n$$ R n

• DOI: 10.1007/s40819-017-0367-8
• Publication Date: 2017-05-22T23:16:48Z
• Authors: B. Parvathalu; P. Sam Johnson
• Keywords: Equiangular polygon

In this article, Mercedes–Benz (MB) frame having 3 vectors in $${\mathbb {R}}^2$$ is generalized to the space $${\mathbb {R}}^n$$ with $$n+1$$ vectors through a complete concrete method. A necessary and sufficient condition for a normed tight frame to be an MB frame is given and MB frame is explored with the help of diagram vectors. In a new approach, it has been proved that there is no MB frame in $${\mathbb {R}}^n$$ with more than $$n+1$$ vectors and there is always an equiangular tight frame for every $$n \ge 2$$ , using MB frame.