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The 369 general32 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 only 369 can be used to build solid burrs. Following is a list of these 369 pieces:

# Piece type Weight Internal Corners Full Back
1

1111
1111
11
11

 
    +----+----+----+----+----+----+
   /                             /|
  +                             + |
 /                             /  +
+----+----+----+----+----+----+   |
|                             |   |
|                             |   +
+                             +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
notchable32
notchable
millable32
millable
general32
general
burr3
 12 0 *
18

0111
0111
11
11

 
    +----+    +----+----+----+----+
   /    /|   /                   /|
  +    + |  +                   + |
 /    /  +-/                   /  +
+----+  / +----+----+----+----+   |
|    | +  |                   |   |
|    |/   |                   |   +
+    +----+                   +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
notchable32
notchable
millable32
millable
general32
general
 10 0 *
20

0111
0011
11
11

 
    +----+    +----+----+----+----+
   /    /|   /                   /|
  +    + |  +----+              + |
 /    /  +--|   /              /  +
+----+  /   |  +----+----+----+   |
|    | +    +--|              |   |
|    |/        |              |   +
+    +----+----+              +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 9 1 *
22

0111
0101
11
11

 
    +----+    +----+----+----+----+
   /    /|   /                   /|
  +    + |  +    +----+         + |
 /    /  +-/    /|   /         /  +
+----+  / +----+ |  +----+----+   |
|    | +  |    | +--|         |   |
|    |/   |    |/   |         |   +
+    +----+    +----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 9 2 *
24

0111
0001
11
11

 
    +----+    +----+----+----+----+
   /    /|   /                   /|
  +    + |  +----+----+         + |
 /    /  +--|        /         /  +
+----+  /   |       +----+----+   |
|    | +    +----+--|         |   |
|    |/             |         |   +
+    +----+----+----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 8 1 *
35

1011
1011
11
11

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

1011
0011
11
11

 
    +----+----+    +----+----+----+
   /         /|   /              /|
  +    +----+ |  +              + |
 /    /|    | +-/              /  +
+----+ |    |/ +----+----+----+   |
|    | +----+  |              |   |
|    |/        |              |   +
+    +----+----+              +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 9 1 *
39

1011
1001
11
11

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

1011
0001
11
11

 
    +----+----+    +----+----+----+
   /         /|   /              /|
  +    +----+ |  +----+         + |
 /    /|    | +--|   /         /  +
+----+ |    |/   |  +----+----+   |
|    | +----+    +--|         |   |
|    |/             |         |   +
+    +----+----+----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 8 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 *
60

0011
0010
11
11

 
    +----+         +----+----+----+
   /    /|        /              /|
  +    + |       +    +----+    + |
 /    /  +----+-/    /|   /    /  +
+----+  /      +----+ |  +----+   |
|    | +       |    | +--|    |   |
|    |/        |    |/   |    |   +
+    +----+----+    +----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 7 2 *
64

0011
0000
11
11

 
    +----+         +----+----+----+
   /    /|        /              /|
  +    + |       +----+----+    + |
 /    /  +----+--|        /    /  +
+----+  /        |       +----+   |
|    | +         +----+--|    |   |
|    |/                  |    |   +
+    +----+----+----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 6 1 *
71

1101
1001
11
11

 
    +----+----+----+    +----+----+
   /              /|   /         /|
  +         +----+ |  +         + |
 /         /|    | +-/         /  +
+----+----+ |    |/ +----+----+   |
|         | +----+  |         |   |
|         |/        |         |   +
+         +----+----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
burr3
 9 1 *
79

1101
1000
11
11

 
    +----+----+----+    +----+----+
   /              /|   /         /|
  +         +----+ |  +----+    + |
 /         /|    | +--|   /    /  +
+----+----+ |    |/   |  +----+   |
|         | +----+    +--|    |   |
|         |/             |    |   +
+         +----+----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 8 2 *
82

0101
0111
11
11

 
    +----+    +----+    +----+----+
   /    /|   /    /|   /         /|
  +    + |  +    +----+         + |
 /    /  +-/                   /  +
+----+  / +----+----+----+----+   |
|    | +  |                   |   |
|    |/   |                   |   +
+    +----+                   +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 9 2 *
84

0101
0011
11
11

 
    +----+    +----+    +----+----+
   /    /|   /    /|   /         /|
  +    + |  +----+----+         + |
 /    /  +--|   /              /  +
+----+  /   |  +----+----+----+   |
|    | +    +--|              |   |
|    |/        |              |   +
+    +----+----+              +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 8 3 *
86

0101
0101
11
11

 
    +----+    +----+    +----+----+
   /    /|   /    /|   /         /|
  +    + |  +    + |  +         + |
 /    /  +-/    /  +-/         /  +
+----+  / +----+  / +----+----+   |
|    | +  |    | +  |         |   |
|    |/   |    |/   |         |   +
+    +----+    +----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
notchable32
notchable
millable32
millable
general32
general
 8 0 *
88

0101
0001
11
11

 
    +----+    +----+    +----+----+
   /    /|   /    /|   /         /|
  +    + |  +----+ |  +         + |
 /    /  +--|    | +-/         /  +
+----+  /   |    |/ +----+----+   |
|    | +    +----+  |         |   |
|    |/             |         |   +
+    +----+----+----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
millable32
millable
general32
general
 7 0 *
94

0101
0100
11
11

 
    +----+    +----+    +----+----+
   /    /|   /    /|   /         /|
  +    + |  +    + |  +----+    + |
 /    /  +-/    /  +--|   /    /  +
+----+  / +----+  /   |  +----+   |
|    | +  |    | +    +--|    |   |
|    |/   |    |/        |    |   +
+    +----+    +----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 7 1 *
96

0101
0000
11
11

 
    +----+    +----+    +----+----+
   /    /|   /    /|   /         /|
  +    + |  +----+ |  +----+    + |
 /    /  +--|    | +--|   /    /  +
+----+  /   |    |/   |  +----+   |
|    | +    +----+    +--|    |   |
|    |/                  |    |   +
+    +----+----+----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 6 1 *
100

1001
0011
11
11

 
    +----+----+         +----+----+
   /         /|        /         /|
  +    +----+ |  +----+         + |
 /    /|    | +-/              /  +
+----+ |    |/ +----+----+----+   |
|    | +----+  |              |   |
|    |/        |              |   +
+    +----+----+              +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 8 2 *
103

1001
1001
11
11

 
    +----+----+         +----+----+
   /         /|        /         /|
  +         + |       +         + |
 /         /  +----+-/         /  +
+----+----+  /      +----+----+   |
|         | +       |         |   |
|         |/        |         |   +
+         +----+----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
notchable32
notchable
millable32
millable
general32
general
burr3
 8 0 *
104

1001
0001
11
11

 
    +----+----+         +----+----+
   /         /|        /         /|
  +    +----+ |       +         + |
 /    /|    | +----+-/         /  +
+----+ |    |/      +----+----+   |
|    | +----+       |         |   |
|    |/             |         |   +
+    +----+----+----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 7 1 *
111

1001
1000
11
11

 
    +----+----+         +----+----+
   /         /|        /         /|
  +         + |       +----+    + |
 /         /  +----+--|   /    /  +
+----+----+  /        |  +----+   |
|         | +         +--|    |   |
|         |/             |    |   +
+         +----+----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 7 1 *
112

1001
0000
11
11

 
    +----+----+         +----+----+
   /         /|        /         /|
  +    +----+ |       +----+    + |
 /    /|    | +----+--|   /    /  +
+----+ |    |/        |  +----+   |
|    | +----+         +--|    |   |
|    |/                  |    |   +
+    +----+----+----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 6 2 *
114

0001
0111
11
11

 
    +----+              +----+----+
   /    /|             /         /|
  +    + |  +----+----+         + |
 /    /  +-/                   /  +
+----+  / +----+----+----+----+   |
|    | +  |                   |   |
|    |/   |                   |   +
+    +----+                   +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 8 1 *
116

0001
0011
11
11

 
    +----+              +----+----+
   /    /|             /         /|
  +    + |       +----+         + |
 /    /  +----+-/              /  +
+----+  /      +----+----+----+   |
|    | +       |              |   |
|    |/        |              |   +
+    +----+----+              +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 7 1 *
118

0001
0101
11
11

 
    +----+              +----+----+
   /    /|             /         /|
  +    + |  +----+    +         + |
 /    /  +-/    /|-+-/         /  +
+----+  / +----+ |  +----+----+   |
|    | +  |    | +  |         |   |
|    |/   |    |/   |         |   +
+    +----+    +----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
millable32
millable
general32
general
 7 0 *
120

0001
0001
11
11

 
    +----+              +----+----+
   /    /|             /         /|
  +    + |            +         + |
 /    /  +----+----+-/         /  +
+----+  /           +----+----+   |
|    | +            |         |   |
|    |/             |         |   +
+    +----+----+----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
notchable32
notchable
millable32
millable
general32
general
 6 0 *
124

0001
0010
11
11

 
    +----+              +----+----+
   /    /|             /         /|
  +    + |       +----+----+    + |
 /    /  +----+-/    /|   /    /  +
+----+  /      +----+ |  +----+   |
|    | +       |    | +--|    |   |
|    |/        |    |/   |    |   +
+    +----+----+    +----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 6 3 *
126

0001
0100
11
11

 
    +----+              +----+----+
   /    /|             /         /|
  +    + |  +----+    +----+    + |
 /    /  +-/    /|-+--|   /    /  +
+----+  / +----+ |    |  +----+   |
|    | +  |    | +    +--|    |   |
|    |/   |    |/        |    |   +
+    +----+    +----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 6 1 *
128

0001
0000
11
11

 
    +----+              +----+----+
   /    /|             /         /|
  +    + |            +----+    + |
 /    /  +----+----+--|   /    /  +
+----+  /             |  +----+   |
|    | +              +--|    |   |
|    |/                  |    |   +
+    +----+----+----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 5 1 *
154

0110
0110
11
11

 
    +----+    +----+----+    +----+
   /    /|   /         /|   /    /|
  +    + |  +         + |  +    + |
 /    /  +-/         /  +-/    /  +
+----+  / +----+----+  / +----+   |
|    | +  |         | +  |    |   |
|    |/   |         |/   |    |   +
+    +----+         +----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
notchable32
notchable
millable32
millable
general32
general
 8 0 *
156

0110
0010
11
11

 
    +----+    +----+----+    +----+
   /    /|   /         /|   /    /|
  +    + |  +----+    + |  +    + |
 /    /  +--|   /    /  +-/    /  +
+----+  /   |  +----+  / +----+   |
|    | +    +--|    | +  |    |   |
|    |/        |    |/   |    |   +
+    +----+----+    +----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 7 1 *
158

0110
0100
11
11

 
    +----+    +----+----+    +----+
   /    /|   /         /|   /    /|
  +    + |  +    +----+ |  +    + |
 /    /  +-/    /|    | +-/    /  +
+----+  / +----+ |    |/ +----+   |
|    | +  |    | +----+  |    |   |
|    |/   |    |/        |    |   +
+    +----+    +----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 7 1 *
160

0110
0000
11
11

 
    +----+    +----+----+    +----+
   /    /|   /         /|   /    /|
  +    + |  +----+----+ |  +    + |
 /    /  +--|         | +-/    /  +
+----+  /   |         |/ +----+   |
|    | +    +----+----+  |    |   |
|    |/                  |    |   +
+    +----+----+----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
millable32
millable
general32
general
 6 0 *
172

1010
0010
11
11

 
    +----+----+    +----+    +----+
   /         /|   /    /|   /    /|
  +    +----+ |  +    + |  +    + |
 /    /|    | +-/    /  +-/    /  +
+----+ |    |/ +----+  / +----+   |
|    | +----+  |    | +  |    |   |
|    |/        |    |/   |    |   +
+    +----+----+    +----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 7 1 *
176

1010
0000
11
11

 
    +----+----+    +----+    +----+
   /         /|   /    /|   /    /|
  +    +----+ |  +----+ |  +    + |
 /    /|    | +--|    | +-/    /  +
+----+ |    |/   |    |/ +----+   |
|    | +----+    +----+  |    |   |
|    |/                  |    |   +
+    +----+----+----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 6 1 *
180

0010
0011
11
11

 
    +----+         +----+    +----+
   /    /|        /    /|   /    /|
  +    + |       +    +----+    + |
 /    /  +----+-/              /  +
+----+  /      +----+----+----+   |
|    | +       |              |   |
|    |/        |              |   +
+    +----+----+              +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 7 2 *
184

0010
0001
11
11

 
    +----+         +----+    +----+
   /    /|        /    /|   /    /|
  +    + |       +----+----+    + |
 /    /  +----+--|   /         /  +
+----+  /        |  +----+----+   |
|    | +         +--|         |   |
|    |/             |         |   +
+    +----+----+----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 6 3 *
188

0010
0010
11
11

 
    +----+         +----+    +----+
   /    /|        /    /|   /    /|
  +    + |       +    + |  +    + |
 /    /  +----+-/    /  +-/    /  +
+----+  /      +----+  / +----+   |
|    | +       |    | +  |    |   |
|    |/        |    |/   |    |   +
+    +----+----+    +----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
notchable32
notchable
millable32
millable
general32
general
 6 0 *
190

0010
0100
11
11

 
    +----+         +----+    +----+
   /    /|        /    /|   /    /|
  +    + |  +----+----+ |  +    + |
 /    /  +-/    /|    | +-/    /  +
+----+  / +----+ |    |/ +----+   |
|    | +  |    | +----+  |    |   |
|    |/   |    |/        |    |   +
+    +----+    +----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 6 2 *
192

0010
0000
11
11

 
    +----+         +----+    +----+
   /    /|        /    /|   /    /|
  +    + |       +----+ |  +    + |
 /    /  +----+--|    | +-/    /  +
+----+  /        |    |/ +----+   |
|    | +         +----+  |    |   |
|    |/                  |    |   +
+    +----+----+----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
millable32
millable
general32
general
 5 0 *
208

1100
0000
11
11

 
    +----+----+----+         +----+
   /              /|        /    /|
  +    +----+----+ |       +    + |
 /    /|         | +----+-/    /  +
+----+ |         |/      +----+   |
|    | +----+----+       |    |   |
|    |/                  |    |   +
+    +----+----+----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 6 1 *
216

0100
0001
11
11

 
    +----+    +----+         +----+
   /    /|   /    /|        /    /|
  +    + |  +----+ |  +----+    + |
 /    /  +--|    | +-/         /  +
+----+  /   |    |/ +----+----+   |
|    | +    +----+  |         |   |
|    |/             |         |   +
+    +----+----+----+         +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 6 1 *
220

0100
0010
11
11

 
    +----+    +----+         +----+
   /    /|   /    /|        /    /|
  +    + |  +----+----+    +    + |
 /    /  +--|   /    /|-+-/    /  +
+----+  /   |  +----+ |  +----+   |
|    | +    +--|    | +  |    |   |
|    |/        |    |/   |    |   +
+    +----+----+    +----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 6 2 *
224

0100
0000
11
11

 
    +----+    +----+         +----+
   /    /|   /    /|        /    /|
  +    + |  +----+ |       +    + |
 /    /  +--|    | +----+-/    /  +
+----+  /   |    |/      +----+   |
|    | +    +----+       |    |   |
|    |/                  |    |   +
+    +----+----+----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
millable32
millable
general32
general
 5 0 *
240

1000
0000
11
11

 
    +----+----+              +----+
   /         /|             /    /|
  +    +----+ |            +    + |
 /    /|    | +----+----+-/    /  +
+----+ |    |/           +----+   |
|    | +----+            |    |   |
|    |/                  |    |   +
+    +----+----+----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
general32
general
 5 1 *
256

0000
0000
11
11

 
    +----+                   +----+
   /    /|                  /    /|
  +    + |                 +    + |
 /    /  +----+----+----+-/    /  +
+----+  /                +----+   |
|    | +                 |    |   |
|    |/                  |    |   +
+    +----+----+----+----+    +  /
|                             | +
|                             |/
+----+----+----+----+----+----+
notchable32
notchable
millable32
millable
general32
general
 4 0 *
274

0111
0111
11
01

 
    +----+    +----+----+----+----+
   /    /|   /                   /|
  +    + |  +                   + |
 /    /  +-/                   /  +
+----+  / +----+----+----+----+   |
|    | +  |                   |   |
|    |/   |                   |   +
+    +----+----+              +  /
|         | +--|              | +
|         |/   |              |/
+----+----+    +----+----+----+
general32
general
 9 2  
276

0111
0011
11
01

 
    +----+    +----+----+----+----+
   /    /|   /                   /|
  +    + |  +----+              + |
 /    /  +--|   /              /  +
+----+  /   |  +----+----+----+   |
|    | +    +  |              |   |
|    |/    /|  |              |   +
+    +----+ |  +              +  /
|         | +--|              | +
|         |/   |              |/
+----+----+    +----+----+----+
notchable
millable32
millable
general32
general
 8 0  
278

0111
0101
11
01

 
    +----+    +----+----+----+----+
   /    /|   /                   /|
  +    + |  +    +----+         + |
 /    /  +-/    /|   /         /  +
+----+  / +----+ |  +----+----+   |
|    | +  |    | +--|         |   |
|    |/   |    |/   |         |   +
+    +----+----+----+         +  /
|         | +--|              | +
|         |/   |              |/
+----+----+    +----+----+----+
general32
general
 8 4  
280

0111
0001
11
01

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