Why a Shamrock?

"St. Patrick's use of the three-leafed shamrock—which he used to explain the Holy Trinity (Father, Son, and Holy Spirit)—played a role in converting early Irish people to Christianity." 

Bing

A better word to use than "trinity" would be Triune Godhead...
And God said let US make man after OUR image, 

after OUR likeness.....
The grace of the Lord Jesus Christ,
and the love of God,
and the fellowship of the Holy Spirit,
be with you all......
Genesis 1:26/2 Corinthians 13:14