Three-piece burr pieces
For regular three piece burrs we are looking at rods of the size 2*2*6. We use the more common length of 6 in preference over the minimal size 4. Since the core of a three piece burr is 8 (Lemma 4.1.1), there are potentially 28=256 possible rods. By excluding disjoint and duplicate rods there are exactly 28 unique ones, of which 9 are notchable. Following is an exhaustive list of all possible regular rods for three piece burrs:
| # | Piece | type | R1 | R2 | R3 | R4 | R5 | R6 | R7 |
|---|---|---|---|---|---|---|---|---|---|
| 1 1111 |
+----+----+----+----+----+----+
/ /|
+ + |
/ / +
+----+----+----+----+----+----+ |
| | |
| | +
+ + /
| | +
| |/
+----+----+----+----+----+----+
|
notchable32 notchable millable32 millable general32 general burr3 |
1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 3 1111 |
+----+----+----+----+----+----+
/ /|
+ +----+ + |
/ /| / / +
+----+----+ | +----+----+----+ |
| | +--| | |
| |/ | | +
+ +----+ + /
| | +
| |/
+----+----+----+----+----+----+
|
general burr3 |
33 | 1025 | 257 | 65 | 2049 | 513 | 5 |
| 7 1111 |
+----+----+----+----+----+----+
/ /|
+ +----+----+ + |
/ /| / / +
+----+----+ | +----+----+ |
| | +----+--| | |
| |/ | | +
+ +----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
|
general burr3 |
97 | 3073 | 769 | 97 | 3073 | 769 | 7 |
| 35 1011 |
+----+----+ +----+----+----+
/ /| / /|
+ + | + + |
/ / +-/ / +
+----+----+ / +----+----+----+ |
| | + | | |
| |/ | | +
+ +----+ + /
| | +
| |/
+----+----+----+----+----+----+
|
notchable32 notchable millable32 millable general32 general burr3 |
1057 | 1281 | 259 | 69 | 2113 | 2561 | 517 |
| 37 1011 |
+----+----+ +----+----+----+
/ /| / /|
+ +----+----+ + |
/ /| / / +
+----+----+----+ | +----+----+ |
| | +--| | |
| |/ | | +
+ +----+ + /
| | +
| |/
+----+----+----+----+----+----+
|
general burr3 |
1089 | 2305 | 515 | 37 | 1089 | 2305 | 515 |
| 39 1011 |
+----+----+ +----+----+----+
/ /| / /|
+ + | +----+ + |
/ / +--| / / +
+----+----+ / | +----+----+ |
| | + +--| | |
| |/ | | +
+ +----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
|
general32 general burr3 |
1121 | 3329 | 771 | 101 | 3137 | 2817 | 519 |
| 67 1101 |
+----+----+----+ +----+----+
/ /| / /|
+ +----+----+ + |
/ /| / / +
+----+----+ | +----+----+----+ |
| | +--| | |
| |/ | | +
+ +----+ + /
| | +
| |/
+----+----+----+----+----+----+
|
general burr3 |
2081 | 1537 | 261 | 67 | 2081 | 1537 | 261 |
| 71 1101 |
+----+----+----+ +----+----+
/ /| / /|
+ +----+ | + + |
/ /| | +-/ / +
+----+----+ | |/ +----+----+ |
| | +----+ | | |
| |/ | | +
+ +----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
|
general32 general burr3 |
2145 | 3585 | 773 | 99 | 3105 | 1793 | 263 |
| 103 1001 |
+----+----+ +----+----+
/ /| / /|
+ + | + + |
/ / +----+-/ / +
+----+----+ / +----+----+ |
| | + | | |
| |/ | | +
+ +----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
|
notchable32 notchable millable32 millable general32 general burr3 |
3169 | 3841 | 775 | 103 | 3169 | 3841 | 775 |
| 289 1011 |
+----+----+ +----+----+----+
/ /| / /|
+ +----+ + |
/ / +
+----+----+----+----+----+----+ |
| | |
| | +
+ +----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
general burr3 |
1027 | 289 | 1027 | 2053 | 577 | 2053 | 577 |
| 291 1011 |
+----+----+ +----+----+----+
/ /| / /|
+ + | + + |
/ / +-/ / +
+----+----+ / +----+----+----+ |
| | +--| | |
| | | | | +
+ + | + + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
notchable millable32 millable general32 general burr3 |
1059 | 1313 | 1283 | 2117 | 2625 | 2565 | 581 |
| 293 1011 |
+----+----+ +----+----+----+
/ /| / /|
+ +----+----+ + |
/ /| / / +
+----+----+----+ | +----+----+ |
| | +--| | |
| |/ | | +
+ +----+----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
general burr3 |
1091 | 2337 | 1539 | 2085 | 1601 | 2309 | 579 |
| 295 1011 |
+----+----+ +----+----+----+
/ /| / /|
+ + | +----+ + |
/ / +--| / / +
+----+----+ / | +----+----+ |
| | +----+--| | |
| | | / | | +
+ + | +----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
general32 general burr3 |
1123 | 3361 | 1795 | 2149 | 3649 | 2821 | 583 |
| 321 1101 |
+----+----+----+ +----+----+
/ /| / /|
+ +----+ + |
/ / +
+----+----+----+----+----+----+ |
| | |
| | +
+ +----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
general burr3 |
2051 | 545 | 1029 | 2051 | 545 | 1029 | 321 |
| 323 1101 |
+----+----+----+ +----+----+
/ /| / /|
+ +----+----+ + |
/ /| / / +
+----+----+ | +----+----+----+ |
| | + | | |
| | | | | +
+ + | + + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
general32 general burr3 |
2083 | 1569 | 1285 | 2115 | 2593 | 1541 | 325 |
| 327 1101 |
+----+----+----+ +----+----+
/ /| / /|
+ +----+ | + + |
/ /| | +-/ / +
+----+----+ | |/ +----+----+ |
| | + + | | |
| | | / | | +
+ + | +----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
notchable millable32 millable general32 general burr3 |
2147 | 3617 | 1797 | 2147 | 3617 | 1797 | 327 |
| 353 1001 |
+----+----+ +----+----+
/ /| / /|
+ +----+----+ + |
/ / +
+----+----+----+----+----+----+ |
| | |
| | +
+ +----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
general burr3 |
3075 | 801 | 1031 | 2055 | 609 | 3077 | 833 |
| 355 1001 |
+----+----+ +----+----+
/ /| / /|
+ + | +----+ + |
/ / +-/ / +
+----+----+ / +----+----+----+ |
| | +--| | |
| | | | | +
+ + | + + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
general32 general burr3 |
3107 | 1825 | 1287 | 2119 | 2657 | 3589 | 837 |
| 357 1001 |
+----+----+ +----+----+
/ /| / /|
+ +----+ + + |
/ /|-+-/ / +
+----+----+----+ | +----+----+ |
| | + | | |
| |/ | | +
+ +----+----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
general32 general burr3 |
3139 | 2849 | 1543 | 2087 | 1633 | 3333 | 835 |
| 359 1001 |
+----+----+ +----+----+
/ /| / /|
+ + | + + |
/ / +----+-/ / +
+----+----+ / +----+----+ |
| | +----+ | | |
| | | / | | +
+ + | +----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
notchable32 notchable millable32 millable general32 general burr3 |
3171 | 3873 | 1799 | 2151 | 3681 | 3845 | 839 |
| 547 1011 |
+----+----+ +----+----+----+
/ /| / /|
+ + | + + |
/ / +-/ / +
+----+----+ / +----+----+----+ |
| | + | | |
| |/ | | +
+ +----+----+ + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
|
general32 general burr3 |
1061 | 1345 | 2307 | 1093 | 2369 | 2563 | 549 |
| 551 1011 |
+----+----+ +----+----+----+
/ /| / /|
+ + | +----+ + |
/ / +--| / / +
+----+----+ / | +----+----+ |
| | + + | | |
| |/ /| | | +
+ +----+ | + + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
|
notchable millable32 millable general32 general burr3 |
1125 | 3393 | 2819 | 1125 | 3393 | 2819 | 551 |
| 611 1001 |
+----+----+ +----+----+
/ /| / /|
+ + | +----+ + |
/ / +-/ / +
+----+----+ / +----+----+----+ |
| | + | | |
| |/ | | +
+ +----+----+ + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
|
general32 general burr3 |
3109 | 1857 | 2311 | 1095 | 2401 | 3587 | 805 |
| 613 1001 |
+----+----+ +----+----+
/ /| / /|
+ +----+ + + |
/ /|-+-/ / +
+----+----+----+ | +----+----+ |
| | +--| | |
| | | | | +
+ + | + + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
|
general32 general burr3 |
3141 | 2881 | 2567 | 1063 | 1377 | 3331 | 803 |
| 615 1001 |
+----+----+ +----+----+
/ /| / /|
+ + | + + |
/ / +----+-/ / +
+----+----+ / +----+----+ |
| | + +--| | |
| |/ /| | | +
+ +----+ | + + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
|
notchable32 notchable millable32 millable general32 general burr3 |
3173 | 3905 | 2823 | 1127 | 3425 | 3843 | 807 |
| 865 1001 |
+----+----+ +----+----+
/ /| / /|
+ +----+----+ + |
/ / +
+----+----+----+----+----+----+ |
| | |
| | +
+ +----+----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
general burr3 |
3079 | 865 | 3079 | 3079 | 865 | 3079 | 865 |
| 867 1001 |
+----+----+ +----+----+
/ /| / /|
+ + | +----+ + |
/ / +-/ / +
+----+----+ / +----+----+----+ |
| | +--| | |
| | | | | +
+ + | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
general32 general burr3 |
3111 | 1889 | 3335 | 3143 | 2913 | 3591 | 869 |
| 871 1001 |
+----+----+ +----+----+
/ /| / /|
+ + | + + |
/ / +----+-/ / +
+----+----+ / +----+----+ |
| | +----+--| | |
| | | | | +
+ + | + + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
notchable32 notchable millable32 millable general32 general burr3 |
3175 | 3937 | 3847 | 3175 | 3937 | 3847 | 871 |
Total notchable : 3
notchable32: 6 (SubTotal: 9)
millable : 0
millable32 : 0 (SubTotal: 9)
general : 9
general32 : 10 (SubTotal: 28)
-----------------
total : 28
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