One, Two, Buckle My Shoe

The Dentist Was Found With A Blackened Hole Below His Right Temple. A Pistol Lay On The Floor Near His Outflung Right Hand. Later, One Of His Patients Was Found Dead From A Lethal Dose Of Local Anaesthetic. A Clear Case Of Murder And Suicide. But Why Would A Dentist Commit A Crime In The Middle Of A Busy Day Of Appointments? A Shoe Buckle Holds The Key To The Mystery. Now In The Words Of The Rhyme Can Poirot Pick Up The Sticks And Lay Them Straight?