Yet another match-up finding: now it is of the remarkable single trailer war bonnet cat # E73150 from Smithsonian (NMNH). As the Museum card says, the bonnet is "Sioux, ca 1880, and was the one used on a model that was used on the 1899 Five dollar bill."
In terms of its construction this war bonnet is made of a felt skullcap. The eagle feathers of the crown have white fluffs at the base, are accented with white gypsum and tipped with horsetail tufts. There is a long row of white ermine tubes as side pendants, lined with the upper side of the browband. The beaded browband features dark blue stepped triangles on a white background. The trailer of red cloth strouding, backed and bordered with canvas, is embellished with eagle down feathers (now missing). IMHO, it looks more 1870s Cheyenne, rather than Sioux.
There is a number of well-known early 20th century photographs that show different Lakota and non-Lakota Indians wearing this bonnet.