# The vertices of the platonic solids are tight frames

## Richard Vale and Shayne Waldron

## Abstract:

Here we give a simple proof that many highly symmetric configurations
of vectors, such as the n-th roots of unity in R^2
and the vertices of the platonic solids in R^3, are tight frames.

**Keywords:**
Tight frames, vertices of the platonic solids

**Math Review Classification:**
Primary 05B20, 33C50, 20C15, 42C15 ;
Secondary 52B15, 42C40

**Length:** 4 pages

**Last Updated:** 2 February 2004

## Availability: