Is Unit McGee rigid?

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I figured out a unit distance embedding for the McGee graph.

Bram Cohen asked me if it's rigid. I had a hard enough time figuring out this one embedding. If some points can move around, I might want to add some more edges. But that would break some existing records in chromatic graphs, if it's not rigid. If it is rigid, then it's a girth 7 rigid object.

Is it rigid?

McGee graph