The 59 notchable six-piece burr pieces
For regular six piece burrs we are looking at rods of the size 2*2*6. Since each piece can have 12 of the 24 cubes removed there are potentially 212=4096 possible pieces. By excluding disjoint and duplicate rods there are exactly 837 unique ones, of which 59 are notchable. Of those 59 notchable ones, only 25 can be used to build solid burrs. Following is a list of all 59 notchable pieces:
| # | Piece | type | Weight | Internal Corners | Full Back |
|---|---|---|---|---|---|
| 1 1111 |
+----+----+----+----+----+----+
/ /|
+ + |
/ / +
+----+----+----+----+----+----+ |
| | |
| | +
+ + /
| | +
| |/
+----+----+----+----+----+----+
|
notchable32 notchable millable32 millable general32 general burr3 |
12 | 0 | * |
| 18 0111 |
+----+ +----+----+----+----+
/ /| / /|
+ + | + + |
/ / +-/ / +
+----+ / +----+----+----+----+ |
| | + | | |
| |/ | | +
+ +----+ + /
| | +
| |/
+----+----+----+----+----+----+
|
notchable32 notchable millable32 millable general32 general |
10 | 0 | * |
| 35 1011 |
+----+----+ +----+----+----+
/ /| / /|
+ + | + + |
/ / +-/ / +
+----+----+ / +----+----+----+ |
| | + | | |
| |/ | | +
+ +----+ + /
| | +
| |/
+----+----+----+----+----+----+
|
notchable32 notchable millable32 millable general32 general burr3 |
10 | 0 | * |
| 52 0011 |
+----+ +----+----+----+
/ /| / /|
+ + | + + |
/ / +----+-/ / +
+----+ / +----+----+----+ |
| | + | | |
| |/ | | +
+ +----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
|
notchable32 notchable millable32 millable general32 general |
8 | 0 | * |
| 86 0101 |
+----+ +----+ +----+----+
/ /| / /| / /|
+ + | + + | + + |
/ / +-/ / +-/ / +
+----+ / +----+ / +----+----+ |
| | + | | + | | |
| |/ | |/ | | +
+ +----+ +----+ + /
| | +
| |/
+----+----+----+----+----+----+
|
notchable32 notchable millable32 millable general32 general |
8 | 0 | * |
| 103 1001 |
+----+----+ +----+----+
/ /| / /|
+ + | + + |
/ / +----+-/ / +
+----+----+ / +----+----+ |
| | + | | |
| |/ | | +
+ +----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
|
notchable32 notchable millable32 millable general32 general burr3 |
8 | 0 | * |
| 120 0001 |
+----+ +----+----+
/ /| / /|
+ + | + + |
/ / +----+----+-/ / +
+----+ / +----+----+ |
| | + | | |
| |/ | | +
+ +----+----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
|
notchable32 notchable millable32 millable general32 general |
6 | 0 | * |
| 154 0110 |
+----+ +----+----+ +----+
/ /| / /| / /|
+ + | + + | + + |
/ / +-/ / +-/ / +
+----+ / +----+----+ / +----+ |
| | + | | + | | |
| |/ | |/ | | +
+ +----+ +----+ + /
| | +
| |/
+----+----+----+----+----+----+
|
notchable32 notchable millable32 millable general32 general |
8 | 0 | * |
| 188 0010 |
+----+ +----+ +----+
/ /| / /| / /|
+ + | + + | + + |
/ / +----+-/ / +-/ / +
+----+ / +----+ / +----+ |
| | + | | + | | |
| |/ | |/ | | +
+ +----+----+ +----+ + /
| | +
| |/
+----+----+----+----+----+----+
|
notchable32 notchable millable32 millable general32 general |
6 | 0 | * |
| 256 0000 |
+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+----+-/ / +
+----+ / +----+ |
| | + | | |
| |/ | | +
+ +----+----+----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
|
notchable32 notchable millable32 millable general32 general |
4 | 0 | * |
| 276 0111 |
+----+ +----+----+----+----+
/ /| / /|
+ + | +----+ + |
/ / +--| / / +
+----+ / | +----+----+----+ |
| | + + | | |
| |/ /| | | +
+ +----+ | + + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
notchable millable32 millable general32 general |
8 | 0 | |
| 291 1011 |
+----+----+ +----+----+----+
/ /| / /|
+ + | + + |
/ / +-/ / +
+----+----+ / +----+----+----+ |
| | +--| | |
| | | | | +
+ + | + + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
notchable millable32 millable general32 general burr3 |
9 | 0 | |
| 308 0011 |
+----+ +----+----+----+
/ /| / /|
+ + | + + |
/ / +----+-/ / +
+----+ / +----+----+----+ |
| | + +--| | |
| |/ /| | | +
+ +----+ | + + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
notchable millable32 millable general32 general |
7 | 0 | |
| 327 1101 |
+----+----+----+ +----+----+
/ /| / /|
+ +----+ | + + |
/ /| | +-/ / +
+----+----+ | |/ +----+----+ |
| | + + | | |
| | | / | | +
+ + | +----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
notchable millable32 millable general32 general burr3 |
8 | 0 | |
| 344 0101 |
+----+ +----+ +----+----+
/ /| / /| / /|
+ + | +----+ | + + |
/ / +--| | +-/ / +
+----+ / | |/ +----+----+ |
| | + + + | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
notchable millable32 millable general32 general |
6 | 0 | |
| 359 1001 |
+----+----+ +----+----+
/ /| / /|
+ + | + + |
/ / +----+-/ / +
+----+----+ / +----+----+ |
| | +----+ | | |
| | | / | | +
+ + | +----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
notchable32 notchable millable32 millable general32 general burr3 |
7 | 0 | |
| 376 0001 |
+----+ +----+----+
/ /| / /|
+ + | + + |
/ / +----+----+-/ / +
+----+ / +----+----+ |
| | + +----+ | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
notchable millable32 millable general32 general |
5 | 0 | |
| 395 1110 |
+----+----+----+----+ +----+
/ /| / /|
+ +----+ + | + + |
/ /| / / +-/ / +
+----+----+ | +----+ / +----+ |
| | + | | + | | |
| | | | |/ | | +
+ + | + +----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
notchable millable32 millable general32 general |
8 | 0 | |
| 412 0110 |
+----+ +----+----+ +----+
/ /| / /| / /|
+ + | +----+ + | + + |
/ / +--| / / +-/ / +
+----+ / | +----+ / +----+ |
| | + + | | + | | |
| |/ /| | |/ | | +
+ +----+ | + +----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
notchable millable32 millable general32 general |
6 | 0 | |
| 427 1010 |
+----+----+ +----+ +----+
/ /| / /| / /|
+ + | + + | + + |
/ / +-/ / +-/ / +
+----+----+ / +----+ / +----+ |
| | +--| | + | | |
| | | | |/ | | +
+ + | + +----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
notchable millable32 millable general32 general |
7 | 0 | |
| 444 0010 |
+----+ +----+ +----+
/ /| / /| / /|
+ + | + + | + + |
/ / +----+-/ / +-/ / +
+----+ / +----+ / +----+ |
| | + +--| | + | | |
| |/ /| | |/ | | +
+ +----+ | + +----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
notchable millable32 millable general32 general |
5 | 0 | |
| 463 1100 |
+----+----+----+ +----+
/ /| / /|
+ +----+ | + + |
/ /| | +----+-/ / +
+----+----+ | |/ +----+ |
| | + + | | |
| | | / | | +
+ + | +----+----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
notchable millable32 millable general32 general |
6 | 0 | |
| 480 0100 |
+----+ +----+ +----+
/ /| / /| / /|
+ + | +----+ | + + |
/ / +--| | +----+-/ / +
+----+ / | |/ +----+ |
| | + + + | | |
| |/ /| / | | +
+ +----+ | +----+----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
notchable millable32 millable general32 general |
4 | 0 | |
| 495 1000 |
+----+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+-/ / +
+----+----+ / +----+ |
| | +----+ | | |
| | | / | | +
+ + | +----+----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
notchable millable32 millable general32 general |
5 | 0 | |
| 512 0000 |
+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+----+-/ / +
+----+ / +----+ |
| | + +----+ | | |
| |/ /| / | | +
+ +----+ | +----+----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
notchable millable32 millable general32 general |
3 | 0 | |
| 534 0111 |
+----+ +----+----+----+----+
/ /| / /|
+ + | + +----+ + |
/ / +-/ /| / / +
+----+ / +----+ | +----+----+ |
| | + | | + | | |
| |/ | | | | | +
+ +----+ + | + + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
|
notchable millable32 millable general32 general |
8 | 0 | |
| 551 1011 |
+----+----+ +----+----+----+
/ /| / /|
+ + | +----+ + |
/ / +--| / / +
+----+----+ / | +----+----+ |
| | + + | | |
| |/ /| | | +
+ +----+ | + + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
|
notchable millable32 millable general32 general burr3 |
8 | 0 | |
| 568 0011 |
+----+ +----+----+----+
/ /| / /|
+ + | +----+ + |
/ / +----+--| / / +
+----+ / | +----+----+ |
| | + + | | |
| |/ /| | | +
+ +----+----+ | + + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
|
notchable millable32 millable general32 general |
6 | 0 | |
| 598 0101 |
+----+ +----+ +----+----+
/ /| / /| / /|
+ + | + + | + + |
/ / +-/ / +-/ / +
+----+ / +----+ / +----+----+ |
| | + | | +--| | |
| |/ | | | | | +
+ +----+ + | + + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
|
notchable millable32 millable general32 general |
7 | 0 | |
| 615 1001 |
+----+----+ +----+----+
/ /| / /|
+ + | + + |
/ / +----+-/ / +
+----+----+ / +----+----+ |
| | + +--| | |
| |/ /| | | +
+ +----+ | + + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
|
notchable32 notchable millable32 millable general32 general burr3 |
7 | 0 | |
| 632 0001 |
+----+ +----+----+
/ /| / /|
+ + | + + |
/ / +----+----+-/ / +
+----+ / +----+----+ |
| | + +--| | |
| |/ /| | | +
+ +----+----+ | + + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
|
notchable millable32 millable general32 general |
5 | 0 | |
| 653 1110 |
+----+----+----+----+ +----+
/ /| / /|
+ +----+ | + + |
/ /| | +-/ / +
+----+----+----+ | |/ +----+ |
| | + + | | |
| | | / | | +
+ + | +----+ + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
|
notchable millable32 millable general32 general |
8 | 0 | |
| 670 0110 |
+----+ +----+----+ +----+
/ /| / /| / /|
+ + | + +----+ | + + |
/ / +-/ /| | +-/ / +
+----+ / +----+ | |/ +----+ |
| | + | | + + | | |
| |/ | | | / | | +
+ +----+ + | +----+ + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
|
notchable millable32 millable general32 general |
6 | 0 | |
| 687 1010 |
+----+----+ +----+ +----+
/ /| / /| / /|
+ + | +----+ | + + |
/ / +--| | +-/ / +
+----+----+ / | |/ +----+ |
| | + + + | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
|
notchable millable32 millable general32 general |
6 | 0 | |
| 704 0010 |
+----+ +----+ +----+
/ /| / /| / /|
+ + | +----+ | + + |
/ / +----+--| | +-/ / +
+----+ / | |/ +----+ |
| | + + + | | |
| |/ /| / | | +
+ +----+----+ | +----+ + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
|
notchable millable32 millable general32 general |
4 | 0 | |
| 717 1100 |
+----+----+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+-/ / +
+----+----+----+ / +----+ |
| | +----+ | | |
| | | / | | +
+ + | +----+ + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
|
notchable millable32 millable general32 general |
7 | 0 | |
| 734 0100 |
+----+ +----+ +----+
/ /| / /| / /|
+ + | + + | + + |
/ / +-/ / +----+-/ / +
+----+ / +----+ / +----+ |
| | + | | +----+ | | |
| |/ | | | / | | +
+ +----+ + | +----+ + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
|
notchable millable32 millable general32 general |
5 | 0 | |
| 751 1000 |
+----+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+-/ / +
+----+----+ / +----+ |
| | + +----+ | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
|
notchable millable32 millable general32 general |
5 | 0 | |
| 768 0000 |
+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+----+-/ / +
+----+ / +----+ |
| | + +----+ | | |
| |/ /| / | | +
+ +----+----+ | +----+ + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
|
notchable millable32 millable general32 general |
3 | 0 | |
| 792 0111 |
+----+ +----+----+----+----+
/ /| / /|
+ + | +----+----+ + |
/ / +--| / / +
+----+ / | +----+----+ |
| | + + | | |
| |/ /| | | +
+ +----+ | + + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
notchable32 notchable millable32 millable general32 general |
6 | 0 | |
| 824 0011 |
+----+ +----+----+----+
/ /| / /|
+ + | +----+ + |
/ / +----+--| / / +
+----+ / | +----+----+ |
| | + +----+ | | |
| |/ /| | | +
+ +----+ | + + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
notchable32 notchable millable32 millable general32 general |
5 | 0 | |
| 856 0101 |
+----+ +----+ +----+----+
/ /| / /| / /|
+ + | +----+ | + + |
/ / +--| | +-/ / +
+----+ / | |/ +----+----+ |
| | + + +--| | |
| |/ /| | | +
+ +----+ | + + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
notchable32 notchable millable32 millable general32 general |
5 | 0 | |
| 871 1001 |
+----+----+ +----+----+
/ /| / /|
+ + | + + |
/ / +----+-/ / +
+----+----+ / +----+----+ |
| | +----+--| | |
| | | | | +
+ + | + + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
notchable32 notchable millable32 millable general32 general burr3 |
6 | 0 | |
| 888 0001 |
+----+ +----+----+
/ /| / /|
+ + | + + |
/ / +----+----+-/ / +
+----+ / +----+----+ |
| | + +----+--| | |
| |/ /| | | +
+ +----+ | + + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
notchable32 notchable millable32 millable general32 general |
4 | 0 | |
| 911 1110 |
+----+----+----+----+ +----+
/ /| / /|
+ +----+----+ | + + |
/ /| | +-/ / +
+----+----+ | |/ +----+ |
| | + + | | |
| | | / | | +
+ + | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
notchable32 notchable millable32 millable general32 general |
6 | 0 | |
| 928 0110 |
+----+ +----+----+ +----+
/ /| / /| / /|
+ + | +----+----+ | + + |
/ / +--| | +-/ / +
+----+ / | |/ +----+ |
| | + + + | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
notchable32 notchable millable32 millable general32 general |
4 | 0 | |
| 943 1010 |
+----+----+ +----+ +----+
/ /| / /| / /|
+ + | +----+ | + + |
/ / +--| | +-/ / +
+----+----+ / | |/ +----+ |
| | +----+ + | | |
| | | / | | +
+ + | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
notchable32 notchable millable32 millable general32 general |
5 | 0 | |
| 960 0010 |
+----+ +----+ +----+
/ /| / /| / /|
+ + | +----+ | + + |
/ / +----+--| | +-/ / +
+----+ / | |/ +----+ |
| | + +----+ + | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
notchable32 notchable millable32 millable general32 general |
3 | 0 | |
| 975 1100 |
+----+----+----+ +----+
/ /| / /|
+ +----+ | + + |
/ /| | +----+-/ / +
+----+----+ | |/ +----+ |
| | + +----+ | | |
| | | / | | +
+ + | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
notchable32 notchable millable32 millable general32 general |
5 | 0 | |
| 992 0100 |
+----+ +----+ +----+
/ /| / /| / /|
+ + | +----+ | + + |
/ / +--| | +----+-/ / +
+----+ / | |/ +----+ |
| | + + +----+ | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
notchable32 notchable millable32 millable general32 general |
3 | 0 | |
| 1007 1000 |
+----+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+-/ / +
+----+----+ / +----+ |
| | +----+----+ | | |
| | | / | | +
+ + | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
notchable32 notchable millable32 millable general32 general |
4 | 0 | |
| 1024 0000 |
+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+----+-/ / +
+----+ / +----+ |
| | + +----+----+ | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
notchable32 notchable millable32 millable general32 general |
2 | 0 | |
| 1417 1110 |