These at first glance appear to be incomplete or weakly struck die trials of the Illinois Centennial design. The illustrated piece was examined at the 2002 ANA sale. It appears that some kind of ring surrounded the obverse and reverse dies preventing the outer portions of the planchet from receiving any detail.
These were probably deliberately struck as a collectors item as opposed to being some kind of setup trials for spacing the dies.
Examples are known as follows:
Copper J2005/P2062 with two examples known, of different striking qualities as follows:
1) 58 ANA lot 2041, Cox-Stacks 4/62 lot 2297, Bowers and Merena's 7/02 - illustrated above. This is believed to be the first one struck as it is weaker than the one below.
Photo courtesy of Bowers and Merena.
2) Cox-Stacks 4/62 lot 2298, Boosel lot 1194.
Nickel J2006/P2063 with the only example known ex Cox-Stacks 4/62 lot 2299. It is stronger in strike than either copper example and is illustrated below.
Photo is a scan from Stacks' R.E. Cox sale.
White Metal J2007/P2064 An example is listed by Taxay as ex Nagy.