You have a Concert model, made between 1899 and 1908.  In my experience
they are pretty rare -- I recall seeing just one in several years at
the Union, IL phono fest -- and I believe I saw one or two cylinders.
I hope you have or can find some.

The purpose of the large Concert 5" cylinder was to get more volume and
higher fidelity.  Once the Amberol cylinders were introduced (in the
usual 2" diameter), Edison discontinued the Concert but, according to
his usual policy, continued to sell conversion kits up through 1913
to let Concert owners play normal sized records on their machines.
All this is from George L. Frow's "Edison Cylinder Phonograph Companion"
book, a must for any cylinder machine collector.

Mike Knudsen