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## Homework Statement

The group of symmetries of a regular pentagram is isomorphic to the dihedral group of order 10.

Show that this is true.

## The Attempt at a Solution

It seems to me that the group shown by the "star" has order 5, since, by following the lines from one point, it takes 5 total paths to get back to the original point.

So I thought it would isomorphic to the cyclic group of order 5.....how is it isomorphic to the dihedral group?