The Homburg hat is the hat famously worn by Winston Churchill and popular with Gangsters.
The homburg is a formal hat that started to become worn from around 1890 when people like King Edward VII wore one.
Dwight Eisenhower and Anthony Eden also famously wore the Homburg as did Al Pachino in Gangster films which resulted in gaining the nickname the Godfather
The hat is identified by a single dent running down the centre of the crown, called a gutter crown, a darker coloured band around the bottom of the crown and stiff curled up brim.
It is a wool felt hat that usually comes in dark colour, grey is the most popular
The hat gets its name from Bad Homburg a district in Germany where Edward VII brought the hat back to Britain from.
I don't own a cigar, so went for the pipe for my photos.