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Piece Orientation  a subset of the 12 cubes pictured in Figure 1 which results in a physically connected piece. Of the 2**12 such combinations, 2225 are connected and 1871 are disconnected.
Piece (or physical piece)  one of the 837 physically different shapes which are represented by the 2225 piece orientations. One piece may produce as many as 8 piece orientations.
Cube Configuration  an assignment of each of the 32 cubes in
Figure 2
to one of the 2 or 3 pieces which may occupy that cube or to
empty space. The number of cube configurations is:
4^8 * 3^24 = 18,509,302,102,818,816
Assembly  A cube configuration in which each of the 6 piece orientations is a physically connected piece. The term 'legal configuration' has also been used this way.
FullyRotated Assembly  for counting purposes, an assembly in the sense above. An orientation is implied in this definition.
Physical Assembly  for counting purposes, two physical assemblies are the same if one can be rotated to match the other.
Logical Assembly  two assemblies are the same logical assembly if one can be rotated and/or reflected to produce the second. If a logical assembly has no internal symmetry, then it is equivalent to 2 physical assemblies and 24 fullyrotated assemblies.
Move  the linear movement of one or more pieces as a group. The direction must be parallel to one of the 3 axes and the distance must be some multiple of the cube width in length.
Solution  an assembly which can be physically disassembled into the 6 individual pieces by a series of moves.
Level of Solution  the minimum number of moves required in order to separate the assembly into at least two parts.
Leveltype  solution levels for an assembly using length6, length8, length10 and length12 pieces. (e.g. leveltype 2300 means level 2 with length 6 pieces; level 3 with length 8 pieces, and no solution with length 10 or longer.)
Partial Solution  an assembly which can be split into at least two parts with moves (described above). Complete disassembly may or may not be possible.
Unique Solution  the physical pieces which are used to make a particular assembly can frequently be used to make other, different assemblies. If only one of the assemblies which can be formed from these pieces has a solution (can be taken completely apart), then this solution is called a unique solution.
Assembly with Movement  some moves with the pieces are possibly, but no disassembly is possible.
State  an arrangement of the pieces which can be reached by moves as described above. A state is uniquely described by the displacements of each piece in the 3 directions from its original position, with one of the 6 pieces being held fixed.
Notchable Piece  a piece which can be cut from a square rod of wood by making cuts perpendicular to the axis of the rod with repeated passes of a regular blade or with a dado blade. Generally speaking, notchable pieces have no "inside" corners or other areas that would require chiseling parts out or gluing cubes in.
Notchable Assembly (Solution)  an assembly (solution) in which each of the 6 pieces is notchable.
Ambiguous Piece  a piece which can be rotated about its long axis in more than one way for placement in an assembled 6piece burr without creating external holes.
Apart Code  a shorthand notation for denoting the method for removing the first piece from an assembly. This allows for easy comparison of moves between two different assemblies.
GENDA (GENeral DisAssembly program)  used to analyze interlocking puzzles built up from cubes to see if they can be taken apart.
FDA (Fast Disassembly Analysis)  a fast version of the GENDA program which finds partial solutions of 6piece burrs only.
BURR6  an assembly & disassembly program used for 6piece burrs. The program determines all ways 6 given pieces can be assembled into a 6piece burr, and then uses the GENDA routines to complete the analysis.
MATR  formula for converting a physical 6piece burr piece with some of its 12 cubes removed into a number from 14096. The resulting matrix can then be used to quickly rule out disconnected pieces, identify duplicate pieces, and other tasks. See section III.C.
LL  a simple, compact way of representing a 6piece burr assembly. It consists of 32 1digit numbers from 06. See Section IV.D. and the Love's Dozen and Computer's Choice Unique10 examples.
JRM (for Journal of Recreational Mathematics)  earliest 6piece burr analysis which was restricted to solid, notchable solutions. See [3].
SCIAM (for Scientific American)  analysis of solid, general (unnotchable) 6piece burr solutions. See [2], [4] and [7].
NOTC  analysis of holey, notchable 6piece burrs.
HB6  analysis of holey, general 6piece burrs.
GB6  first phase of HB6 analysis which was used to analyze holey 6piece burrs with from 0 to 5 holes.
IB6  programs used in the HB6 analysis for assemblies with from 16 to 20 holes.
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