Table 1  -  Summary of 6-Piece Burr Analyses

Analysis           JRM      SCIAM       NOTC           HB6

Notchable ?        yes        no         yes            no
Solid ?           solid     solid       holey         holey

Pieces

Different           25       369         59            837
Complete Set        42       485        ? (a)          ? (a)
Piece Orientations  50       790        147           2225

Solutions

Logical            179      60,186    7.4 million  5.75 billion (b)
Physical           314     119,979   14.8 million 11.50 billion (b)

Partial Solutions & Solutions

Logical            181      78,777    7,458,937    5,951,254,866
Physical           318     157,122   14,913,154   11,902,446,737

Assemblies

Logical            588  25,062,952   13,354,991   35,657,131,235
Physical         1,063  50,122,724   26,704,015   71,314,165,174
Fully-Rotated   12,597 601,456,869  320,439,782  855,769,655,392

Cube Configuration Counts

        Solid      110,075,314,176  Holey 18,509,302,102,818,816

Maximum Solution Levels

                level=1  level=1      maximum=10   maximum=12
                                       unique=5     unique=10

Reference    JRM [3] SCIAM [2],[4],[7]  ---this booklet---

Notes:

     (a) The number of pieces for a complete set to construct all
possible holey 6-piece burrs is of little interest.  Pieces with few
cubes can be used with many duplicates, but the resulting assemblies
would be loose and fall apart easily.  In addition, many interesting
assemblies need pieces of length 8, 10 or 12, so a complete set would
consist of different lengths of most piece shapes as well as duplicates.

     (b) Counts for complete solutions remain unknown.  The numbers
here are estimates based on complete analysis of a random sample of
5,588 un-notchable assemblies.