Further to ycaso’s post dating the uniform c1920 and your point about “Someone” indicating the buttons being incompatible with a rank of corporal.
No doubt there will be others but for me the only button rank insignia I’m familiar with are Royal Navy, that today is limited to the senior rating of Chief Petty Officers.
Several web searches for combinations of polish uniform NCO rank cuffs buttons etc., gave several hits that described uniform changes 1919/20 for Polish forces and I’ve posted a couple at the end of this summary:
1] I could not find any reference that related rank to buttons for polish forces.
2] The reference to buttons on cuffs either pre or post 1919 appears to relate to design as being either with buttons or plain; in images most buttoned cuff designs appeared to have 3 buttons.
3] As far as rank insignia for NCOs’ is concerned they would be either horizontal stripes or chevrons that at various times have been on cuffs, upper sleeve or shoulder straps & hats.
4] The hat shown in the picture is showing the two horizontal silver bars of a corporal that are repeated on his shoulder straps.
I think the hats shown in images on this forum depict headgear that could be same as in the photograph.
http://forum.axishistory.com/viewtopic.php?f=53&t=51746&... This link
https://www.google.co.uk/search?tbm=bks&hl=en&q=poli... throws up two Google books of interest.
P49/50 of MILITARY UNIFORMS IN EUROPE 1900 - 2000 Volume One; R Spencer Kidd covers Polish forces and mentions the “considerable variety of uniforms” worn by the Polish army during its early years and the “traditional zigzag” being reinstated to collar patches in 1920
Pages 22-24 of “Armies of the Russo-Polish War 1919–21”; Nigel Thomas, Adam Hook contains as much information to help elimination as help with positive identification. On p24 “Greater Polish Army” there is mention of collar badges depicting army branches of particular interest is “Lancers – regimentally coloured pennants”