There were quite a few military academies across Japan, and I think there were a
lot of varieties, too. Generally, on military cups the Academy Double Star is
prevalent, obviously related to the Army star. (
ARMY). The Naval Academy used the
same Double Star. When you find a Naval Academy cup (which are quite rare),
you'll also see other naval symbols, like an anchor or ship.
Here are three examples of the characters to look for:
GAKKO (school). These are on most Academy cups. As you
can tell by the photos, oftentimes these are hand-written
and difficult to decipher.
SOTSU-GYOU Graduation.
Also found on Academy cups.
SHI-HAN (read right to left):
Instructor. Sometimes found on
Teacher Academy cups.
SHI-KAN (read right to left): Officer
SHIKAN GAKKO is Military Academy
Large Army star. The rim is dark brown.
Inscribed 'Toyohashi Military Academy,
Graduation Commemorative, Otsuka'.
Inscribed 'Infantry Academy Dispatch [Graduation],
24th Infantry Discharge, Mori'.
Near the machine gun is the Military Academy
10-rayed star.
Army Academy 10-point star. Inscribed 'Infantry Academy
Detachment, Commemorative, Suzuki'.

Inscribed 'Infantry Academy, Detachment
Commemorative, Konishi'.
Scarce Engineer Academy cup.
Inscribed 'Dispatch Commemorative, Army Engineer Academy'.
Rare metal cup. The academy's 10-pointed star is at the top.
Inscribed 'Academy Dispatch Commemorative'.
The poem says something like 'Your body is lighter than a
feather, but duty is heavier than a mountain. Do your duty and
you can return home and enjoy the blossoms.'
The design has the 10-pointed Military Academy star.
Inscribed 'Army, Toyama Academy,  Commemorative, Nakao'.  
This school was located in Tokyo. It opened in 1873 and
closed in Septmeber 1945.
Inscribed 'Army Infantry Academy, Dispatch Commemorative'.  
On the reverse '31st Infantry Discharge.'
The design has the Military Academy flag.
Inscribed 'Toyama Academy,  Commemorative'.  
Inscribed 'Army Infantry Academy, Dispatch Commemorative'.  
Rare design.
Inscribed 'Army Infantry Academy.'