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The 837 general 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. Following is a list of these 837 pieces:

# Piece type Weight Internal Corners Full Back
1

1111
1111
11
11

 
    +----+----+----+----+----+----+
   /                             /|
  +                             + |
 /                             /  +
+----+----+----+----+----+----+   |
|                             |   |
|                             |   +
+                             +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
notchable32
notchable
millable32
millable
general32
general
burr3
 12 0 *
2

1111
0111
11
11

 
    +----+----+----+----+----+----+
   /                             /|
  +    +----+                   + |
 /    /|   /                   /  +
+----+ |  +----+----+----+----+   |
|    | +--|                   |   |
|    |/   |                   |   +
+    +----+                   +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 11 2 *
3

1111
1011
11
11

 
    +----+----+----+----+----+----+
   /                             /|
  +         +----+              + |
 /         /|   /              /  +
+----+----+ |  +----+----+----+   |
|         | +--|              |   |
|         |/   |              |   +
+         +----+              +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
burr3
 11 2 *
4

1111
0011
11
11

 
    +----+----+----+----+----+----+
   /                             /|
  +    +----+----+              + |
 /    /|        /              /  +
+----+ |       +----+----+----+   |
|    | +----+--|              |   |
|    |/        |              |   +
+    +----+----+              +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 10 2 *
6

1111
0101
11
11

 
    +----+----+----+----+----+----+
   /                             /|
  +    +----+    +----+         + |
 /    /|   /    /|   /         /  +
+----+ |  +----+ |  +----+----+   |
|    | +--|    | +--|         |   |
|    |/   |    |/   |         |   +
+    +----+    +----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 10 4 *
7

1111
1001
11
11

 
    +----+----+----+----+----+----+
   /                             /|
  +         +----+----+         + |
 /         /|        /         /  +
+----+----+ |       +----+----+   |
|         | +----+--|         |   |
|         |/        |         |   +
+         +----+----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
burr3
 10 2 *
8

1111
0001
11
11

 
    +----+----+----+----+----+----+
   /                             /|
  +    +----+----+----+         + |
 /    /|             /         /  +
+----+ |            +----+----+   |
|    | +----+----+--|         |   |
|    |/             |         |   +
+    +----+----+----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 9 2 *
10

1111
0110
11
11

 
    +----+----+----+----+----+----+
   /                             /|
  +    +----+         +----+    + |
 /    /|   /         /|   /    /  +
+----+ |  +----+----+ |  +----+   |
|    | +--|         | +--|    |   |
|    |/   |         |/   |    |   +
+    +----+         +----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 10 4 *
12

1111
0010
11
11

 
    +----+----+----+----+----+----+
   /                             /|
  +    +----+----+    +----+    + |
 /    /|        /    /|   /    /  +
+----+ |       +----+ |  +----+   |
|    | +----+--|    | +--|    |   |
|    |/        |    |/   |    |   +
+    +----+----+    +----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 9 4 *
16

1111
0000
11
11

 
    +----+----+----+----+----+----+
   /                             /|
  +    +----+----+----+----+    + |
 /    /|                  /    /  +
+----+ |                 +----+   |
|    | +----+----+----+--|    |   |
|    |/                  |    |   +
+    +----+----+----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 8 2 *
18

0111
0111
11
11

 
    +----+    +----+----+----+----+
   /    /|   /                   /|
  +    + |  +                   + |
 /    /  +-/                   /  +
+----+  / +----+----+----+----+   |
|    | +  |                   |   |
|    |/   |                   |   +
+    +----+                   +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
notchable32
notchable
millable32
millable
general32
general
 10 0 *
19

0111
1011
11
11

 
    +----+    +----+----+----+----+
   /    /|   /                   /|
  +    +----+----+              + |
 /         /|   /              /  +
+----+----+ |  +----+----+----+   |
|         | +--|              |   |
|         |/   |              |   +
+         +----+              +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 10 4 *
20

0111
0011
11
11

 
    +----+    +----+----+----+----+
   /    /|   /                   /|
  +    + |  +----+              + |
 /    /  +--|   /              /  +
+----+  /   |  +----+----+----+   |
|    | +    +--|              |   |
|    |/        |              |   +
+    +----+----+              +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 9 1 *
21

0111
1101
11
11

 
    +----+    +----+----+----+----+
   /    /|   /                   /|
  +    +----+    +----+         + |
 /              /|   /         /  +
+----+----+----+ |  +----+----+   |
|              | +--|         |   |
|              |/   |         |   +
+              +----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 10 4 *
22

0111
0101
11
11

 
    +----+    +----+----+----+----+
   /    /|   /                   /|
  +    + |  +    +----+         + |
 /    /  +-/    /|   /         /  +
+----+  / +----+ |  +----+----+   |
|    | +  |    | +--|         |   |
|    |/   |    |/   |         |   +
+    +----+    +----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 9 2 *
23

0111
1001
11
11

 
    +----+    +----+----+----+----+
   /    /|   /                   /|
  +    +----+----+----+         + |
 /         /|        /         /  +
+----+----+ |       +----+----+   |
|         | +----+--|         |   |
|         |/        |         |   +
+         +----+----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 9 4 *
24

0111
0001
11
11

 
    +----+    +----+----+----+----+
   /    /|   /                   /|
  +    + |  +----+----+         + |
 /    /  +--|        /         /  +
+----+  /   |       +----+----+   |
|    | +    +----+--|         |   |
|    |/             |         |   +
+    +----+----+----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 8 1 *
25

0111
1110
11
11

 
    +----+    +----+----+----+----+
   /    /|   /                   /|
  +    +----+         +----+    + |
 /                   /|   /    /  +
+----+----+----+----+ |  +----+   |
|                   | +--|    |   |
|                   |/   |    |   +
+                   +----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 10 4 *
26

0111
0110
11
11

 
    +----+    +----+----+----+----+
   /    /|   /                   /|
  +    + |  +         +----+    + |
 /    /  +-/         /|   /    /  +
+----+  / +----+----+ |  +----+   |
|    | +  |         | +--|    |   |
|    |/   |         |/   |    |   +
+    +----+         +----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 9 2 *
27

0111
1010
11
11

 
    +----+    +----+----+----+----+
   /    /|   /                   /|
  +    +----+----+    +----+    + |
 /         /|   /    /|   /    /  +
+----+----+ |  +----+ |  +----+   |
|         | +--|    | +--|    |   |
|         |/   |    |/   |    |   +
+         +----+    +----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 9 6 *
28

0111
0010
11
11

 
    +----+    +----+----+----+----+
   /    /|   /                   /|
  +    + |  +----+    +----+    + |
 /    /  +--|   /    /|   /    /  +
+----+  /   |  +----+ |  +----+   |
|    | +    +--|    | +--|    |   |
|    |/        |    |/   |    |   +
+    +----+----+    +----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 8 3 *
29

0111
1100
11
11

 
    +----+    +----+----+----+----+
   /    /|   /                   /|
  +    +----+    +----+----+    + |
 /              /|        /    /  +
+----+----+----+ |       +----+   |
|              | +----+--|    |   |
|              |/        |    |   +
+              +----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 9 4 *
30

0111
0100
11
11

 
    +----+    +----+----+----+----+
   /    /|   /                   /|
  +    + |  +    +----+----+    + |
 /    /  +-/    /|        /    /  +
+----+  / +----+ |       +----+   |
|    | +  |    | +----+--|    |   |
|    |/   |    |/        |    |   +
+    +----+    +----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 8 2 *
31

0111
1000
11
11

 
    +----+    +----+----+----+----+
   /    /|   /                   /|
  +    +----+----+----+----+    + |
 /         /|             /    /  +
+----+----+ |            +----+   |
|         | +----+----+--|    |   |
|         |/             |    |   +
+         +----+----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 8 4 *
32

0111
0000
11
11

 
    +----+    +----+----+----+----+
   /    /|   /                   /|
  +    + |  +----+----+----+    + |
 /    /  +--|             /    /  +
+----+  /   |            +----+   |
|    | +    +----+----+--|    |   |
|    |/                  |    |   +
+    +----+----+----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 7 1 *
34

1011
0111
11
11

 
    +----+----+    +----+----+----+
   /         /|   /              /|
  +    +----+----+              + |
 /    /|   /                   /  +
+----+ |  +----+----+----+----+   |
|    | +--|                   |   |
|    |/   |                   |   +
+    +----+                   +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 10 4 *
35

1011
1011
11
11

 
    +----+----+    +----+----+----+
   /         /|   /              /|
  +         + |  +              + |
 /         /  +-/              /  +
+----+----+  / +----+----+----+   |
|         | +  |              |   |
|         |/   |              |   +
+         +----+              +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
notchable32
notchable
millable32
millable
general32
general
burr3
 10 0 *
36

1011
0011
11
11

 
    +----+----+    +----+----+----+
   /         /|   /              /|
  +    +----+ |  +              + |
 /    /|    | +-/              /  +
+----+ |    |/ +----+----+----+   |
|    | +----+  |              |   |
|    |/        |              |   +
+    +----+----+              +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 9 1 *
37

1011
1101
11
11

 
    +----+----+    +----+----+----+
   /         /|   /              /|
  +         +----+----+         + |
 /              /|   /         /  +
+----+----+----+ |  +----+----+   |
|              | +--|         |   |
|              |/   |         |   +
+              +----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
burr3
 10 4 *
38

1011
0101
11
11

 
    +----+----+    +----+----+----+
   /         /|   /              /|
  +    +----+----+----+         + |
 /    /|   /    /|   /         /  +
+----+ |  +----+ |  +----+----+   |
|    | +--|    | +--|         |   |
|    |/   |    |/   |         |   +
+    +----+    +----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 9 6 *
39

1011
1001
11
11

 
    +----+----+    +----+----+----+
   /         /|   /              /|
  +         + |  +----+         + |
 /         /  +--|   /         /  +
+----+----+  /   |  +----+----+   |
|         | +    +--|         |   |
|         |/        |         |   +
+         +----+----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
burr3
 9 1 *
40

1011
0001
11
11

 
    +----+----+    +----+----+----+
   /         /|   /              /|
  +    +----+ |  +----+         + |
 /    /|    | +--|   /         /  +
+----+ |    |/   |  +----+----+   |
|    | +----+    +--|         |   |
|    |/             |         |   +
+    +----+----+----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 8 2 *
42

1011
0110
11
11

 
    +----+----+    +----+----+----+
   /         /|   /              /|
  +    +----+----+    +----+    + |
 /    /|   /         /|   /    /  +
+----+ |  +----+----+ |  +----+   |
|    | +--|         | +--|    |   |
|    |/   |         |/   |    |   +
+    +----+         +----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 9 6 *
43

1011
1010
11
11

 
    +----+----+    +----+----+----+
   /         /|   /              /|
  +         + |  +    +----+    + |
 /         /  +-/    /|   /    /  +
+----+----+  / +----+ |  +----+   |
|         | +  |    | +--|    |   |
|         |/   |    |/   |    |   +
+         +----+    +----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 9 2 *
44

1011
0010
11
11

 
    +----+----+    +----+----+----+
   /         /|   /              /|
  +    +----+ |  +    +----+    + |
 /    /|    | +-/    /|   /    /  +
+----+ |    |/ +----+ |  +----+   |
|    | +----+  |    | +--|    |   |
|    |/        |    |/   |    |   +
+    +----+----+    +----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 8 3 *
45

1011
1100
11
11

 
    +----+----+    +----+----+----+
   /         /|   /              /|
  +         +----+----+----+    + |
 /              /|        /    /  +
+----+----+----+ |       +----+   |
|              | +----+--|    |   |
|              |/        |    |   +
+              +----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 9 4 *
46

1011
0100
11
11

 
    +----+----+    +----+----+----+
   /         /|   /              /|
  +    +----+----+----+----+    + |
 /    /|   /    /|        /    /  +
+----+ |  +----+ |       +----+   |
|    | +--|    | +----+--|    |   |
|    |/   |    |/        |    |   +
+    +----+    +----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 8 6 *
47

1011
1000
11
11

 
    +----+----+    +----+----+----+
   /         /|   /              /|
  +         + |  +----+----+    + |
 /         /  +--|        /    /  +
+----+----+  /   |       +----+   |
|         | +    +----+--|    |   |
|         |/             |    |   +
+         +----+----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 8 1 *
48

1011
0000
11
11

 
    +----+----+    +----+----+----+
   /         /|   /              /|
  +    +----+ |  +----+----+    + |
 /    /|    | +--|        /    /  +
+----+ |    |/   |       +----+   |
|    | +----+    +----+--|    |   |
|    |/                  |    |   +
+    +----+----+----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 7 2 *
50

0011
0111
11
11

 
    +----+         +----+----+----+
   /    /|        /              /|
  +    + |  +----+              + |
 /    /  +-/                   /  +
+----+  / +----+----+----+----+   |
|    | +  |                   |   |
|    |/   |                   |   +
+    +----+                   +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 9 1 *
51

0011
1011
11
11

 
    +----+         +----+----+----+
   /    /|        /              /|
  +    +----+    +              + |
 /         /|-+-/              /  +
+----+----+ |  +----+----+----+   |
|         | +  |              |   |
|         |/   |              |   +
+         +----+              +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 9 1 *
52

0011
0011
11
11

 
    +----+         +----+----+----+
   /    /|        /              /|
  +    + |       +              + |
 /    /  +----+-/              /  +
+----+  /      +----+----+----+   |
|    | +       |              |   |
|    |/        |              |   +
+    +----+----+              +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
notchable32
notchable
millable32
millable
general32
general
 8 0 *
54

0011
0101
11
11

 
    +----+         +----+----+----+
   /    /|        /              /|
  +    + |  +----+----+         + |
 /    /  +-/    /|   /         /  +
+----+  / +----+ |  +----+----+   |
|    | +  |    | +--|         |   |
|    |/   |    |/   |         |   +
+    +----+    +----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 8 3 *
55

0011
1001
11
11

 
    +----+         +----+----+----+
   /    /|        /              /|
  +    +----+    +----+         + |
 /         /|-+--|   /         /  +
+----+----+ |    |  +----+----+   |
|         | +    +--|         |   |
|         |/        |         |   +
+         +----+----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 8 2 *
56

0011
0001
11
11

 
    +----+         +----+----+----+
   /    /|        /              /|
  +    + |       +----+         + |
 /    /  +----+--|   /         /  +
+----+  /        |  +----+----+   |
|    | +         +--|         |   |
|    |/             |         |   +
+    +----+----+----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 7 1 *
58

0011
0110
11
11

 
    +----+         +----+----+----+
   /    /|        /              /|
  +    + |  +----+    +----+    + |
 /    /  +-/         /|   /    /  +
+----+  / +----+----+ |  +----+   |
|    | +  |         | +--|    |   |
|    |/   |         |/   |    |   +
+    +----+         +----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 8 3 *
59

0011
1010
11
11

 
    +----+         +----+----+----+
   /    /|        /              /|
  +    +----+    +    +----+    + |
 /         /|-+-/    /|   /    /  +
+----+----+ |  +----+ |  +----+   |
|         | +  |    | +--|    |   |
|         |/   |    |/   |    |   +
+         +----+    +----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 8 3 *
60

0011
0010
11
11

 
    +----+         +----+----+----+
   /    /|        /              /|
  +    + |       +    +----+    + |
 /    /  +----+-/    /|   /    /  +
+----+  /      +----+ |  +----+   |
|    | +       |    | +--|    |   |
|    |/        |    |/   |    |   +
+    +----+----+    +----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 7 2 *
61

0011
1100
11
11

 
    +----+         +----+----+----+
   /    /|        /              /|
  +    +----+----+----+----+    + |
 /              /|        /    /  +
+----+----+----+ |       +----+   |
|              | +----+--|    |   |
|              |/        |    |   +
+              +----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 8 4 *
62

0011
0100
11
11

 
    +----+         +----+----+----+
   /    /|        /              /|
  +    + |  +----+----+----+    + |
 /    /  +-/    /|        /    /  +
+----+  / +----+ |       +----+   |
|    | +  |    | +----+--|    |   |
|    |/   |    |/        |    |   +
+    +----+    +----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 7 3 *
63

0011
1000
11
11

 
    +----+         +----+----+----+
   /    /|        /              /|
  +    +----+    +----+----+    + |
 /         /|-+--|        /    /  +
+----+----+ |    |       +----+   |
|         | +    +----+--|    |   |
|         |/             |    |   +
+         +----+----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 7 2 *
64

0011
0000
11
11

 
    +----+         +----+----+----+
   /    /|        /              /|
  +    + |       +----+----+    + |
 /    /  +----+--|        /    /  +
+----+  /        |       +----+   |
|    | +         +----+--|    |   |
|    |/                  |    |   +
+    +----+----+----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 6 1 *
66

1101
0111
11
11

 
    +----+----+----+    +----+----+
   /              /|   /         /|
  +    +----+    +----+         + |
 /    /|   /                   /  +
+----+ |  +----+----+----+----+   |
|    | +--|                   |   |
|    |/   |                   |   +
+    +----+                   +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 10 4 *
67

1101
1011
11
11

 
    +----+----+----+    +----+----+
   /              /|   /         /|
  +         +----+----+         + |
 /         /|   /              /  +
+----+----+ |  +----+----+----+   |
|         | +--|              |   |
|         |/   |              |   +
+         +----+              +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
burr3
 10 4 *
68

1101
0011
11
11

 
    +----+----+----+    +----+----+
   /              /|   /         /|
  +    +----+----+----+         + |
 /    /|        /              /  +
+----+ |       +----+----+----+   |
|    | +----+--|              |   |
|    |/        |              |   +
+    +----+----+              +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 9 4 *
70

1101
0101
11
11

 
    +----+----+----+    +----+----+
   /              /|   /         /|
  +    +----+    + |  +         + |
 /    /|   /    /  +-/         /  +
+----+ |  +----+  / +----+----+   |
|    | +--|    | +  |         |   |
|    |/   |    |/   |         |   +
+    +----+    +----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 9 2 *
71

1101
1001
11
11

 
    +----+----+----+    +----+----+
   /              /|   /         /|
  +         +----+ |  +         + |
 /         /|    | +-/         /  +
+----+----+ |    |/ +----+----+   |
|         | +----+  |         |   |
|         |/        |         |   +
+         +----+----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
burr3
 9 1 *
72

1101
0001
11
11

 
    +----+----+----+    +----+----+
   /              /|   /         /|
  +    +----+----+ |  +         + |
 /    /|         | +-/         /  +
+----+ |         |/ +----+----+   |
|    | +----+----+  |         |   |
|    |/             |         |   +
+    +----+----+----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 8 1 *
74

1101
0110
11
11

 
    +----+----+----+    +----+----+
   /              /|   /         /|
  +    +----+    +----+----+    + |
 /    /|   /         /|   /    /  +
+----+ |  +----+----+ |  +----+   |
|    | +--|         | +--|    |   |
|    |/   |         |/   |    |   +
+    +----+         +----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 9 6 *
75

1101
1010
11
11

 
    +----+----+----+    +----+----+
   /              /|   /         /|
  +         +----+----+----+    + |
 /         /|   /    /|   /    /  +
+----+----+ |  +----+ |  +----+   |
|         | +--|    | +--|    |   |
|         |/   |    |/   |    |   +
+         +----+    +----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general
 9 6 *
76

1101
0010
11
11

 
    +----+----+----+    +----+----+
   /              /|   /