| num | old-name | non-isolated | name |
manifold | etc(reduce) | | data |
| empty | | K-1 | T-1 |
$S^3$ | $\Sigma(0,1)$ | ○ |
| | K-2 | T-2 |
$P^3$ | $\Sigma(2,1)$ | ○ |
| 0 | $\sharp0$ | ○ | T0 |
solid torus | | ○ |
| 1 | $\sharp1$ | ◎ | T1 |
$T^2\times I$ | | ○ |
* 1 1 2 * 1 -2 -2
|
| 2 | $\sharp2$ | K2-4 | T2 |
$S^3/Q_8$ | $\Sigma(Q_8)$ | ○ |
* 1 -2 3 -4 * 1 -3 4 -2 * 1 -4 2 -3
|
| 3 | $\sharp3$ | 3 | T3-1 |
$C_3\times S^1$ | | ○ |
* 1 5 -3 * 1 6 -4 * 2 5 -4 * 1 -2 3 -4 3 -6 5 -6 -2
|
| $\sharp3(4^3,6)$ | K3-7 | T3-2 |
$S^3/Q_{12}$ | $\Sigma(Q_{12})$ | ○ |
* 1 -2 3 -4 * 1 5 -6 -2 * 3 -6 5 -4 * 1 6 -4 2 5 -3
|
| 4 | $\sharp4\textrm-2(4^2,6)$ | ○ | T4-1 |
t $I$-bdl/$K$ |
$\rightarrow$$\sharp3_2+\sharp1$ | |
* 1 5 7 -4 * 1 6 -8 -3 * 1 -2 3 -5 -2 * 2 6 -7 8 -4 * 3 7 -8 -5 6 -4
|
| $\sharp4\textrm-1(4^4,8)$ | K4-15 | T4-2 |
$S^3/Q_{16}$ | $\Sigma(Q_{16})$ | ○ |
* 1 -2 3 -4 * 1 5 -6 -2 * 3 7 -8 -4 * 5 -7 8 -6 * 1 6 -7 -4 2 5 -8 -3
|
| $\sharp4\textrm-2(4,5^4)$ | K4-17 | T4-3 |
$S^3/P_{24}$ | $\Sigma(B(2,3,4))$ | ○ |
* 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 | $\sharp5\textrm-2(4^3)$ | ◎ | T5-1 |
|
$\searrow\sharp3+\sharp1_1$
| |
* 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
|
| $\sharp5\textrm-2(4,5^2,6)$ | ○ |
T5-2 |
trefoil |
$\rightarrow\sharp3_1+\sharp1_1+\sharp1$ | |
* 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
|
| $\sharp5\textrm-3(4^2,5^2)$ | ○ |
T5-3 |
t $I$-bdl/$K$ | $\rightarrow$ T4-1$+\sharp1$
| |
* 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
|
| $\sharp5\textrm-1(4^5,10)$ | 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
|
| $\sharp5\textrm-2(4^2,5^2,6^2)$ | K5-46 |
T5-5 |
$S^3/P_{48}$ |
$\rightarrow$ 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
|
| $\sharp5-4(4^3,6^3)$ | K5-49 |
T5-6 |
$S^3/P_{48}$ | $\rightarrow$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
|
| $\sharp5\textrm-4(5^6)$ | K5-50 | T5-7 |
$S^3/P_{120}$ | $\Sigma(B(2,3,5))$ | ○ |
* 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 | $\sharp6\textrm-2(4^2,5^2)$ | ◎ | T6-01 |
| $\searrow\sharp3+\sharp1^2_1$ | |
* 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
|
| $\sharp6\textrm-2(4^2,6^3)$ | ○ | T6-02 |
t I-bdl/K | $\rightarrow$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
|
| $\sharp6\textrm-4(4^3,5^2)$ | ○ | T6-03 |
t I-bdl/K |
$\ra$ 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
|
| $\sharp6\textrm-6(4^2,6)$ | ◎ |
T6-04 |
| $\sea$ #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
|
| $\sharp6\textrm-6(4^2,8)$ | ◎ | T6-05 |
|
$\ra$ 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
|
| $\sharp6\textrm-6(4^2,6^2)$ | ◎ |
T6-06 |
| $\ra$ #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
|
|
$\sharp6\textrm-6(4,5^3,6)$ | ○ | T6-07 |
trefoil | $\ra$
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
|
| $\sharp6\textrm-6(5^4)$ | ◎ | T6-08 |
| $\swarrow$ 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
|
| $\sharp6\textrm-10(4^3)$ | ◎ | T6-09 |
| $\ra$
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
|
| $\sharp6\textrm-11(4^4,9)$ | ○ | T6-10 |
trefoil | $\searrow$ 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
|
| $\sharp6\textrm-11(4^3,5)$ | ◎ | T6-11 |
| $\searrow$ #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
|
| $\sharp6\textrm-11(4^2,6^2)$ | ◎ |
T6-12 |
| $\ra$
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
|
| $\sharp6\textrm-11(4^2)$ | 4 | T6-13 |
$C_4\times S^1$ |
$\ra$ #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
|
| $\sharp6\textrm-11(4)$ | 4 | T6-14 |
$2C_3\times S^1$ |
$\ra$ #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
|
| $\sharp6\textrm-1(4^6,12)$ | K6-136 |
T6-15 |
$S^3/Q_{24}$ | $\Sigma(Q_{24})$ | ○ |
* 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
|
| $\sharp6\textrm-2(4^3,5^2,7^2)$ | K6-137 |
T6-16 |
$S^3/P_{120}$ | $\sea$ 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
|
| $\sharp6\textrm-3(4^6,12)$ | K6-141 |
T6-17 |
| $\sea$ #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
|
| $\sharp6\textrm-3(4^4,6^2,8)$ | K6-142 |
T6-18 |
$S^3/Q_{16}\times \Z_3$ | $\sea$ 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
|
| $\sharp6\textrm-3(4^3,6^4)$ | K6-143 |
T6-19 |
Seifert/$S^2$ | $\ra$
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
|
| $\sharp6\textrm-9(4^3,5^2,7^2)$ | K6-151 |
T6-20 |
$S^3/P_{120}$ | $\sea$ 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
|
| $\sharp6\textrm-11(4^6,12)$ | K6-155 |
T6-21 |
$S^3/P_{120}$ | $\ra$ 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
|
| $\sharp6\textrm-11(4^3,6^4)_2$ | K6-160 |
T6-22 |
Seifert/$S^2$ |
$\ra$
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
|
| $\sharp6\textrm-11(4^3,6^4)_1$ | K6-163 |
T6-23 |
$T^2\times S^1$ | | ○ |
* 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
|
| $\sharp6\textrm-11(4^2,5^2,6^3)_1$ | 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
|
| $\sharp6\textrm-11(4^2,5^2,6^3)_2$ | K6-165 |
T6-25 |
Seifert/$S^2$ | $\ra$ #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
|
| $\sharp6\textrm-11(4,5^4,6^2)$ | K6-166 |
T6-26 |
Seifert/$S^2$ | $\ra$
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
|
| $\sharp6\textrm-11(5^6,6)_1$ | 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
|
| $\sharp6\textrm-11(5^6,6)_2$ | 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
|