This is a nice visual of one of the construction methods using only compass and straightedge...
http://www.mathopenref.com/constinpentagon.html
There are a few instances of the use of pentagons in metalworking fields. Pentagonal valve actuators on fire hydrants are commonly used to prevent tampering and many police shields are five-pointed.
The only septagonal item I've encountered is seven-pointed police shields. Some jurisdictions seem sensitive about offending Jews by using an hexagonal form.

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