Thank You all for the time You spent on this topic.
Jonathan, actually I tried to deal with perspective or/and transformPerspective and the best solution was to put perspective for the container and transformPerspective for each face. 'Doesn't fit' means that the action called with rotationZ or rotationY moves the whole cube whereas the rotationX action rotates each face separately.
PointC, thanks for Your translation
OSUBlake, the rotationX, rotationY and rotationZ actions already animate separately each face. Please, tell me what do You mean about 'be reversed'?
Do You think that the parameters of the command at the beginning transformOrigin:'50% 50% -100px' for each face explains why it works for rotationY & rotationZ and not with rotationX?