Abstract:
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A set of lines through the origin in an Euclidean space is equiangular when any pair of lines from this set intersects with each other at a common angle. This set forms an equiangular tight frame if this angle attains its value given by the Welch bound. The Mercedes-Benz frames in $\Bbb R^m,$ which are special cases of equiangular tight frames, are known to exist. They are presented here by a direct constructive method unlike previously known induction methods or the use of signature matrices. Being full spark frames, they are simplices in R^m. too. The constructive method presented thus constructs simplices in any dimension.
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