| num | old-name | non-isolated | name |
manifold | etc(reduce) | | data |
| empty | | K-1 | T-1 |
S^3 | S(0,1) | ○ |
| | K-2 | T-2 |
P^3 | S(2,1) | ○ |
| 0 | #0 | ○ | T0 |
solid torus | | ○ |
| 1 | #1 | ◎ | T1 |
T^2x I | | ○ |
* 1 1 2 * 1 -2 -2
|
| 2 | #2 | K2-4 | T2 |
S^3/Q_8 | S(Q_8) | ○ |
* 1 -2 3 -4 * 1 -3 4 -2 * 1 -4 2 -3
|
| 3 | #3 | 3 | T3-1 |
C_3x S^1 | | ○ |
* 1 5 -3 * 1 6 -4 * 2 5 -4 * 1 -2 3 -4 3 -6 5 -6 -2
|
| #3(4^3,6) | K3-7 | T3-2 |
S^3/Q_12 | S(Q_12) | ○ |
* 1 -2 3 -4 * 1 5 -6 -2 * 3 -6 5 -4 * 1 6 -4 2 5 -3
|
| 4 | #4-2(4^2,6) | ○ | T4-1 |
t I-bdl/K | ->
#3_2+#1 | |
* 1 5 7 -4 * 1 6 -8 -3 * 1 -2 3 -5 -2 * 2 6 -7 8 -4 * 3 7 -8 -5 6 -4
|
| #4-1(4^4,8) | K4-15 | T4-2 |
S^3/Q_16 | S(Q_16) | ○ |
* 1 -2 3 -4 * 1 5 -6 -2 * 3 7 -8 -4 * 5 -7 8 -6 * 1 6 -7 -4 2 5 -8 -3
|
| #4-2(4,5^4) | K4-17 | T4-3 |
S^3/P_24 | S(B(2,3,4)) | ○ |
* 3 -5 6 -4 * 1 -2 3 7 -4 * 1 5 7 -8 -3 * 1 6 -8 -5 -2 * 2 6 -7 8 -4
|
| 5 | #5-2(4^3) | ◎ | T5-1 |
| > #3+#1_1
| |
* 1 -2 3 -4 * 1 5 -7 -3 * 2 6 -8 -4 * 1 6 -9 -5 -2 * 3 8 -10 -7 -4 * 5 10 -9 -7 8 -9 10 -6
|
| #5-2(4,5^2,6) | ○ |
T5-2 |
trefoil |
=> #3_1+#1_1+#1 | |
* 1 -2 3 -4 * 1 5 9 -6 -2 * 1 6 -10 -7 -3 * 2 5 10 -8 -4 * 7 9 -10 9 -8 * 3 8 -6 5 -7 -4
|
| #5-3(4^2,5^2) | ○ |
T5-3 |
t I-bdl/K | => T4-1+#1
| |
* 1 5 7 -4 * 1 6 -8 -3 * 1 -2 3 -5 -2 * 3 7 9 -10 -4 * 5 8 -10 9 -6 * 2 6 -10 -7 8 -9 -4
|
| #5-1(4^5,10) | K5-43 | T5-4 |
S^3/Q_20 | | ○ |
* 1 -2 3 -4 * 1 5 -6 -2 * 3 7 -8 -4 * 5 9 -10 -6 * 7 -10 9 -8 * 1 6 9 -7 -4 2 5 10 -8 -3
|
| #5-2(4^2,5^2,6^2) | K5-46 |
T5-5 |
S^3/P_48 |
-> T5-6 | ○ |
* 1 -2 3 -4 * 5 -7 8 -6 * 1 5 9 -6 -2 * 3 7 10 -8 -4 * 1 6 -10 9 -8 -3 * 2 5 10 -9 -7 -4
|
| #5-4(4^3,6^3) | K5-49 |
T5-6 |
S^3/P_48 | => T5-5
| △ |
* 1 5 8 -3 * 1 6 10 -4 * 1 7 -9 -2 * 2 -5 6 -8 9 -4 * 2 8 10 -7 6 -3 * 3 10 -9 -5 7 -4
|
| #5-4(5^6) | K5-50 | T5-7 |
S^3/P_120 | S(B(2,3,5)) | ○ |
* 1 5 8 10 -4 * 1 6 10 -9 -2 * 1 7 -9 8 -3 * 2 -5 7 -10 -3 * 2 8 -6 7 -4 * 3 -6 5 9 -4
|
| 6 | #6-2(4^2,5^2) | ◎ | T6-01 |
| > #3+#1^2_1 | |
* 1 -2 3 -4 * 1 5 -6 -2 * 1 6 9 -7 -3 * 2 5 10 -8 -4 * 3 8 -11 -7 -4 * 5 9 12 -10 -6 * 7 12 -11 -9 10 -11 12 -8
|
| #6-2(4^2,6^3) | ○ | T6-02 |
t I-bdl/K | => T5-3+#1
#3_1+#1^2_1+#1 | |
* 1 -2 3 -4 * 1 5 -6 -2 * 3 7 11 -8 -4 * 9 11 -12 11 -10 * 1 6 9 12 -8 -3 * 2 5 10 -12 -7 -4 * 5 9 -7 8 -10 -6
|
| #6-4(4^3,5^2) | ○ | T6-03 |
t I-bdl/K |
=> T5-3+#1 | |
* 1 -2 3 -4 * 5 10 -11 -6 * 7 9 11 -8 * 1 5 9 -6 -2 * 3 8 -10 -7 -4 * 9 12 -11 12 -10 * 1 6 12 -8 -4 2 5 -7 -3
|
| #6-6(4^2,6) | ◎ |
T6-04 |
| > #3_1+2#1
| |
* 1 5 7 -4 * 2 6 -9 -4 * 7 9 11 -8 * 1 6 12 -8 -3 * 9 12 -11 12 -10 * 3 -5 6 11 -10 -4 * 1 -2 3 7 10 -8 -5 -2
|
| #6-6(4^2,8) | ◎ | T6-05 |
|
-> T6-04 | |
* 1 5 7 -4 * 7 9 11 -8 * 1 -2 3 -5 -2 * 1 6 12 -8 -3 * 2 6 11 -10 -4 * 9 12 -11 12 -10 * 3 7 10 -8 -5 6 -9 -4
|
| #6-6(4^2,6^2) | ◎ |
T6-06 |
| => #3_2+#3
| |
* 3 8 -10 -4 * 5 7 9 -6 * 1 -2 1 5 -3 * 9 11 -12 11 -10 * 1 6 11 -8 7 -4 * 2 5 8 -12 -9 -4 * 2 6 12 -10 -7 -3
|
|
#6-6(4,5^3,6) | ○ | T6-07 |
trefoil | =>
T5-2+#1 | |
* 1 5 7 -4 * 1 -2 3 -5 -2 * 1 6 11 -8 -3 * 5 8 -10 9 -6 * 7 10 -11 12 -8 * 2 6 12 -11 -9 -4 * 3 7 9 12 -10 -4
|
| #6-6(5^4) | ◎ | T6-08 |
| < T6-12+#1 | □ |
* 1 -2 1 5 -3 * 2 5 8 -10 -4 * 2 6 -9 -7 -3 * 3 8 -11 -9 -4 * 5 7 10 -11 -6 * 9 12 -11 12 -10 * 1 6 12 -8 7 -4
|
| #6-10(4^3) | ◎ | T6-09 |
| ->
T6-04 | |
* 1 5 -7 -3 * 1 6 -11 -4 * 2 5 -10 -4 * 3 9 -12 -4 * 8 -10 11 -9 * 1 -2 3 8 -7 9 -6 -2 * 5 -8 7 -10 12 -11 12 -6
|
| #6-11(4^4,9) | ○ | T6-10 |
trefoil | > T5-2 | |
* 1 5 8 -4 * 1 7 -9 -2 * 2 8 -10 -3 * 3 11 -12 -4 * 5 9 -12 -10 -6 * 1 6 11 -7 6 -3 * 2 -5 7 -12 -8 9 -11 10 -4
|
| #6-11(4^3,5) | ◎ | T6-11 |
| > #3+#1_1 | |
* 1 5 8 -4 * 1 7 -9 -2 * 8 -10 11 -9 * 2 -5 7 -12 -4 * 2 8 12 -11 -3 * 5 9 -12 -10 -6 * 1 6 11 -7 6 -3 4 -10 -3
|
| #6-11(4^2,6^2) | ◎ |
T6-12 |
| =>
T6-06 | |
* 1 5 8 -4 * 2 9 -11 -3 * 6 10 12 -7 * 1 6 -3 4 -10 -3 * 1 7 -11 10 -8 -2 * 2 -5 6 11 -12 -4 * 5 9 -12 -8 9 -7
|
| #6-11(4^2) | 4 | T6-13 |
C_4x S^1 |
-> #3+#3 | |
* 1 7 -12 -4 * 2 9 -11 -3 * 5 8 -10 -6 * 1 5 -2 1 6 -3 * 2 8 -4 3 10 -4 * 5 9 -7 6 11 -7 * 8 12 -11 10 12 -9
|
| #6-11(4) | 4 | T6-14 |
2C_3x S^1 |
-> #3+#3 | |
* 1 7 -12 -4 * 2 9 -11 -3 * 5 8 -10 -6 * 1 5 -2 1 6 -3 * 2 8 -4 3 10 -4 * 5 9 -12 -8 9 -7 * 6 11 -12 -10 11 -7
|
| #6-1(4^6,12) | K6-136 |
T6-15 |
S^3/Q_24 | S(Q_24) | ○ |
* 1 -2 3 -4 * 1 5 -6 -2 * 3 7 -8 -4 * 5 9 -10 -6 * 7 11 -12 -8 * 9 -11 12 -10 * 1 6 9 -12 -7 -4 2 5 10 -11 -8 -3
|
| #6-2(4^3,5^2,7^2) | K6-137 |
T6-16 |
S^3/P_120 | > T5-7 | |
* 1 -2 3 -4 * 1 5 -6 -2 * 7 -9 10 -8 * 3 7 11 -8 -4 * 5 10 -12 -9 -6 * 1 6 10 -11 12 -8 -3 * 2 5 9 11 -12 -7 -4
|
| #6-3(4^6,12) | K6-141 |
T6-17 |
| > #3_2+#1_1 | |
* 1 -2 3 -4 * 1 5 -7 -3 * 2 6 -8 -4 * 5 9 -11 -6 * 7 10 -12 -8 * 9 -12 11 -10 * 1 6 12 -11 -8 -3 4 7 9 -10 -5 -2
|
| #6-3(4^4,6^2,8) | K6-142 |
T6-18 |
S^3/Q_16x Z_3 | > K5-41 | |
* 1 -2 3 -4 * 1 5 -7 -3 * 2 6 -8 -4 * 9 -11 12 -10 * 1 6 11 -10 -5 -2 * 3 8 12 -9 -7 -4 * 5 9 -10 -7 8 11 -12 -6
|
| #6-3(4^3,6^4) | K6-143 |
T6-19 |
Seifert/S^2 | =>
T6-26 | ○ |
* 1 -2 3 -4 * 5 -7 8 -6 * 9 -11 12 -10 * 1 5 9 -10 -7 -3 * 1 6 11 -10 -5 -2 * 2 6 12 -11 -8 -4 * 3 8 12 -9 -7 -4
|
| #6-9(4^3,5^2,7^2) | K6-151 |
T6-20 |
S^3/P_120 | > T5-7 | |
* 3 8 -10 -4 * 5 -8 9 -6 * 7 11 -12 -8 * 1 -2 3 7 -4 * 1 5 12 -6 -2 * 1 6 -11 10 12 -9 -3 * 2 5 -10 -7 9 -11 -4
|
| #6-11(4^6,12) | K6-155 |
T6-21 |
S^3/P_120 | => T6-16 | |
* 1 5 8 -4 * 1 7 -9 -2 * 2 -5 6 -3 * 3 11 -12 -4 * 6 10 12 -7 * 8 -10 11 -9 * 1 6 11 -7 5 9 -12 -8 -2 4 -10 -3
|
| #6-11(4^3,6^4)_2 | K6-160 |
T6-22 |
Seifert/S^2 |
->
T6-13_4
| |
* 1 5 8 -4 * 2 9 -11 -3 * 6 10 12 -7 * 1 6 11 -12 -8 -2 * 1 7 -9 8 -10 -3 * 2 -5 7 -11 10 -4 * 3 -6 5 9 -12 -4
|
| #6-11(4^3,6^4)_1 | K6-163 |
T6-23 |
T^2x S^1 | | ○ |
* 1 7 -12 -4 * 2 9 -11 -3 * 5 8 -10 -6 * 1 5 9 -12 -10 -3 * 1 6 11 -12 -8 -2 * 2 -5 7 -11 10 -4 * 3 -6 7 -9 8 -4
|
| #6-11(4^2,5^2,6^3)_1 | K6-164 |
T6-24 |
Seifert/S^2 | | ○ |
* 1 5 8 -4 * 6 10 12 -7 * 1 6 11 -9 -2 * 2 -5 7 -11 -3 * 1 7 -9 8 -10 -3 * 2 8 12 -11 10 -4 * 3 -6 5 9 -12 -4
|
| #6-11(4^2,5^2,6^3)_2 | K6-165 |
T6-25 |
Seifert/S^2 | => #3+3#1_1 | |
* 1 7 -12 -4 * 2 9 -11 -3 * 1 5 8 -10 -3 * 2 -5 6 10 -4 * 1 6 11 -12 -8 -2 * 3 -6 7 -9 8 -4 * 5 9 -12 -10 11 -7
|
| #6-11(4,5^4,6^2) | K6-166 |
T6-26 |
Seifert/S^2 | =>
T6-19 | △ |
* 1 7 -12 -4 * 1 5 8 -10 -3 * 1 6 11 -9 -2 * 2 8 12 -11 -3 * 5 9 -12 -10 -6 * 2 -5 7 -9 8 -4 * 3 -6 7 -11 10 -4
|
| #6-11(5^6,6)_1 | K6-167 |
T6-27 |
T^2-bdl/S^1 | | ○ |
* 1 5 8 -10 -3 * 1 6 11 -9 -2 * 1 7 -9 8 -4 * 2 8 12 -11 -3 * 3 -6 7 -12 -4 * 5 9 -12 -10 -6 * 2 -5 7 -11 10 -4
|
| #6-11(5^6,6)_2 | K6-168 |
T6-28 |
T^2-bdl/S^1 | | ○ |
* 1 5 8 -10 -3 * 1 6 11 -9 -2 * 1 7 -11 10 -4 * 2 -5 7 -12 -4 * 2 8 12 -11 -3 * 5 9 -12 -10 -6 * 3 -6 7 -9 8 -4
|