The 

.....vidmahe
....dhimahI
tan naH pracodayAt

type are called various Gayatris not Gayatri mantras.

For example, if the tan nah ............ prachodayat reads as tan nah vishNuh prachodayat it is called VishNu gayatri. 

Gayatri Mantra and these Gayatris of the formula 

.....vidmahe
....dhimahI
tan naH pracodayAt

do not belong to the same category. 

Gayatri mantra is a full , unique, single mantra. 

Where as the Gayatris is a formula that can be used to generate several Gayatris that are never used/executed the way Gayatri Mantra is executed. 

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