Dynabase

Type

Summary of Extreme Examples

For each problem, the most extreme map in the database of each degree, over ℚ and over quadratic fields. When several maps share the record, the first one loaded is shown; the degree links to the full list for that degree. The Mathematical Background page describes each problem.

Rational Preperiodic Points Export to Sage

Many rational preperiodic points Export to Sage

Polynomials over ℚ Export to Sage

Degree Function Field of Definition Preperiodic Points Graph Citations
2 (x2 − 21/16·y2 : y2) 1.1.1.1 9 view WR1994, Poonen1998, Doyle2014, Doyle2018, Doyle2020
3 (2x3 + 3x2y − 8xy2 − 6y3 : 3y3) 1.1.1.1 12 view Benedetto2009, DoHy2025
4 (x4 − 2x3y − 13x2y2 + 14xy3 − 48y4 : 24y4) 1.1.1.1 11 view DoHy2025
5 (4x5 − 20x4y − 5x3y2 + 95x2y3 − 14xy4 − 60y5 : 30y5) 1.1.1.1 14 view DoHy2025
6 (x6 + 21x5y + 115x4y2 − 105x3y3 − 1556x2y4 + 84xy5 − 720y6 : 720y6) 1.1.1.1 15 view DoHy2025
7 (8x7 − 28x6y − 154x5y2 + 455x4y3 + 1022x3y4 − 2002x2y5 − 2451xy6 + 1890y7 : 630y7) 1.1.1.1 16 view DoHy2025
8 (x8 + 20x7y + 70x6y2 − 700x5y3 − 3731x4y4 + 6440x3y5 + 33900x2y6 − 36000xy7 − 20160y8 : 20160y8) 1.1.1.1 17 view DoHy2025
9 (16x9 − 696x7y2 + 9849x5y4 − 49219x3y6 + 57060xy8 − 5670y9 : 11340y9) 1.1.1.1 20 view DoHy2025
10 (x10 + 5x9y − 210x8y2 − 870x7y3 + 15393x6y4 + 49245x5y5 − 450640x4y6 − 984380x3y7 + 4064256x2y8 + 4564800xy9 − 1814400y10 : 1814400y10) 1.1.1.1 21 view DoHy2025
11 (x11 − 205x9y2 + 14883x7y4 − 451795x5y6 + 4987516x3y8 − 8179200xy10 + 3628800y11 : -3628800y11) 1.1.1.1 20 view DoHy2025
12 (x12 − 126x11y + 7049x10y2 − 230790x9y3 + 4906023x8y4 − 70986258x7y5 + 712405427x6y6 − 4956342930x5y7 + 23477770876x4y8 − 72861245016x3y9 + 138251771424x2y10 − 140949607680xy11 + 57131827200y12 : 43545600y12) 1.1.1.1 21 view DoHy2025
13 (x13 − 143x12y + 9178x11y2 − 349206x10y3 + 8761753x9y4 − 152522799x8y5 + 1886334164x7y6 − 16681595788x6y7 + 104670816536x5y8 − 455629039008x4y9 + 1320045298208x3y10 − 2370430947456x2y11 + 2315049903360xy12 − 907588281600y13 : -518918400y13) 1.1.1.1 22 view DoHy2025
14 (34x14 − 5474x13y + 397033x12y2 − 17145856x11y3 + 490911421x10y4 − 9820782972x9y5 + 140949659279x8y6 − 1466929231768x7y7 + 11059905517661x6y8 − 59702976487154x5y9 + 225313258722188x4y10 − 570881108919576x3y11 + 907090218753984x2y12 − 796573394467200xy13 + 285901205990400y14 : 43589145600y14) 1.1.1.1 23 view DoHy2025
15 (41x15 − 7380x14y + 604100x13y2 − 29767920x12y3 + 985137062x11y4 − 23127063960x10y5 + 396533008300x9y6 − 5035984770960x8y7 + 47529555226153x7y8 − 331368195898740x6y9 + 1680182681686600x5y10 − 6029166612225120x4y11 + 14653631890929744x3y12 − 22451626097881920x2y13 + 19048387680000000xy14 − 6585448117248000y15 : 1307674368000y15) 1.1.1.1 24 view DoHy2025

Non-polynomial maps over ℚ Export to Sage

Degree Function Field of Definition Preperiodic Points Graph Citations
2 (x2 + 5xy − 6y2 : x2 + 3xy + 2y2) 1.1.1.1 16 view Vishkautsan2026
3 (130x2y − 55xy2 − 60y3 : -36x3 − 50x2y + 176xy2 − 60y3) 1.1.1.1 13 view Hutz2026
4 (3x4 − 9x2y2 + 48y4 : 7x3y − 28xy3) 1.1.1.1 12 view GHJSX2021
5 (y5 : x5) 1.1.1.1 4 view dFH2018
6 (y6 : x6) 1.1.1.1 4 view dFH2018
7 (y7 : x7) 1.1.1.1 4 view dFH2018
11 (x11 + 66x6y5 − 11xy10 : -11x10y − 66x5y6 + y11) 1.1.1.1 2 view dFH2018

Polynomials over quadratic fields Export to Sage

Degree Function Field of Definition Preperiodic Points Graph Citations
2 (x2 − 21/16·y2 : y2) 2.2.17.1 15 view WR1994, Poonen1998, Doyle2014, Doyle2018, Doyle2020
4 (x4 + y4 : y4) 2.0.3.1 5 view DoHi2025
6 (x6 + (a - 1)y6 : y6) 2.0.3.1 8 view DoHi2025

Long rational cycles Export to Sage

Polynomials over ℚ Export to Sage

Degree Function Field of Definition Longest Cycle Graph Citations
2 (x2 − 301/144·y2 : y2) 1.1.1.1 3 view WR1994, Poonen1998, Doyle2014, Doyle2018, Doyle2020
3 (2x3 + 3x2y − 11xy2 − 6y3 : 6y3) 1.1.1.1 5 view Benedetto2009, Hutz2026
4 (3x4 − 14x3y − 63x2y2 + 314xy3 : -120y4) 1.1.1.1 6 view Hutz2026
5 (172x5 − 280x4y − 1175x3y2 + 1330x2y3 + 1843xy4 − 1050y5 : -420y5) 1.1.1.1 8 view Hutz2026
6 (37x6 + 699x5y + 3955x4y2 + 3345x3y3 − 24152x2y4 − 29244xy5 + 5040y6 : 5040y6) 1.1.1.1 8 view Hutz2026
7 (17x7 − 70x6y − 469x5y2 + 1610x4y3 + 3668x3y4 − 7840x2y5 − 6996xy6 + 2520y7 : 2520y7) 1.1.1.1 10 view Hutz2026
8 (4x8 + 21x7y − 161x6y2 − 651x5y3 + 2611x4y4 + 5754x3y5 − 17574x2y6 − 10164xy7 + 20160y8 : 5040y8) 1.1.1.1 11 view Hutz2026
9 (272x9 + 384x8y − 4536x7y2 − 4704x6y3 + 26481x5y4 + 17976x4y5 − 60269x3y6 − 19326x2y7 + 36162xy8 − 3780y9 : -7560y9) 1.1.1.1 11 view Hutz2026
10 (74x10 − 238x9y − 52401x8y2 − 618552x7y3 − 699552x6y4 + 17285898x5y5 + 37024291x4y6 − 138284468x3y7 − 36272412x2y8 − 8112240xy9 − 129729600y10 : -129729600y10) 1.1.1.1 12 view Hutz2026
11 (257x11 + 9331x10y + 120130x9y2 + 579300x8y3 − 229479x7y4 − 11442417x6y5 − 52169780x5y6 − 128719150x4y7 + 428342072x3y8 + 2215246536x2y9 − 1413900000xy10 − 1037836800y11 : -518918400y11) 1.1.1.1 13 view Hutz2026
12 (6847x12 − 246252x11y + 2861183x10y2 − 4657620x9y3 − 133640139x8y4 + 716294124x7y5 + 1338002189x6y6 − 14257305420x5y7 + 2892624592x4y8 + 88929820128x3y9 − 36791713872x2y10 − 129870336960xy11 − 108972864000y12 : -21794572800y12) 1.1.1.1 14 view Hutz2026
13 (860x13 + 61685x12y + 1906138x11y2 + 33008833x10y3 + 347125350x9y4 + 2213680755x8y5 + 7633125214x7y6 + 5859546979x6y7 − 52599293890x5y8 − 171757668940x4y9 − 108558503352x3y10 + 204127005888x2y11 + 181197233280xy12 + 6227020800y13 : -6227020800y13) 1.1.1.1 15 view Hutz2026
14 (34x14 − 5474x13y + 397033x12y2 − 17145856x11y3 + 490911421x10y4 − 9820782972x9y5 + 140949659279x8y6 − 1466929231768x7y7 + 11059905517661x6y8 − 59702976487154x5y9 + 225313258722188x4y10 − 570881108919576x3y11 + 907090218753984x2y12 − 796573394467200xy13 + 285901205990400y14 : 43589145600y14) 1.1.1.1 1 view DoHy2025
15 (41x15 − 7380x14y + 604100x13y2 − 29767920x12y3 + 985137062x11y4 − 23127063960x10y5 + 396533008300x9y6 − 5035984770960x8y7 + 47529555226153x7y8 − 331368195898740x6y9 + 1680182681686600x5y10 − 6029166612225120x4y11 + 14653631890929744x3y12 − 22451626097881920x2y13 + 19048387680000000xy14 − 6585448117248000y15 : 1307674368000y15) 1.1.1.1 4 view DoHy2025

Non-polynomial maps over ℚ Export to Sage

Degree Function Field of Definition Longest Cycle Graph Citations
2 (380x2 + 913xy − 1878y2 : 95x2 − 583xy − 1806y2) 1.1.1.1 7 view BCHKW2014
3 (38x3 + 37x2y − 39xy2 − 24y3 : -8x3 + 7x2y − 11xy2 − 12y3) 1.1.1.1 8 view Hutz2026
4 (12x4 + 5x3y + 321x2y2 + 126xy3 − 104y4 : -18x4 + 6x3y + 98x2y2 + 80xy3 + 104y4) 1.1.1.1 10 view Hutz2026
5 (y5 : x5) 1.1.1.1 2 view dFH2018
6 (y6 : x6) 1.1.1.1 2 view dFH2018
7 (y7 : x7) 1.1.1.1 2 view dFH2018
11 (x11 + 66x6y5 − 11xy10 : -11x10y − 66x5y6 + y11) 1.1.1.1 1 view dFH2018

Polynomials over quadratic fields Export to Sage

Degree Function Field of Definition Longest Cycle Graph Citations
2 (x2 − 71/48·y2 : y2) 2.2.33.1 6 view Stoll2008, Hutz2013, Doyle2014, Doyle2018
4 (x4 + y4 : y4) 2.0.3.1 2 view DoHi2025
6 (x6 + (a - 1)y6 : y6) 2.0.3.1 1 view DoHi2025

Long rational tails Export to Sage

Polynomials over ℚ Export to Sage

Degree Function Field of Definition Longest Tail Graph Citations
2 (x2 − 2y2 : y2) 1.1.1.1 2 view WR1994, Poonen1998, Ingram2012, Doyle2014, Lukas2014, Doyle2018, Doyle2020
3 (x3 + 3x2y − 10xy2 − 6y3 : 6y3) 1.1.1.1 4 view Benedetto2009, Hutz2026
4 (7x4 + 6x3y − 67x2y2 − 186xy3 + 120y4 : 120y4) 1.1.1.1 5 view Hutz2026
5 (52x5 + 60x4y − 305x3y2 − 45x2y3 − 242xy4 − 465y5 : -630y5) 1.1.1.1 6 view Hutz2026
6 (3x6 + 49x5y + 185x4y2 − 365x3y3 − 1868x2y4 + 1156xy5 + 840y6 : -840y6) 1.1.1.1 7 view Hutz2026
7 (2x7 − 35x6y + 161x5y2 + 70x4y3 − 1477x3y4 + 2485x2y5 − 3726xy6 : 2520y7) 1.1.1.1 9 view Hutz2026
8 (9x8 − 140x7y + 434x6y2 + 2296x5y3 − 10759x4y4 − 11900x3y5 + 50636x2y6 + 90384xy7 − 80640y8 : -40320y8) 1.1.1.1 9 view Hutz2026
9 (19x9 − 326x8y + 1027x7y2 + 8440x6y3 − 43145x5y4 − 57044x4y5 + 370923x3y6 + 215250x2y7 − 162504xy8 − 332640y9 : 332640y9) 1.1.1.1 10 view Hutz2026
10 (848x10 + 7920x9y − 15400x8y2 − 154440x7y3 + 94149x6y4 + 980595x5y5 − 255200x4y6 − 2280960x3y7 + 353353x2y8 + 1550835xy9 − 177750y10 : 207900y10) 1.1.1.1 11 view Hutz2026
11 (2076x11 + 66177x10y + 718525x9y2 + 2134860x8y3 − 13169922x7y4 − 90177339x6y5 − 36287115x5y6 + 681611190x4y7 + 1044667796x3y8 − 853094088x2y9 − 2812145760xy10 + 2075673600y11 : -518918400y11) 1.1.1.1 12 view Hutz2026
12 (16391x12 − 673482x11y + 10411807x10y2 − 67309050x9y3 + 35206113x8y4 + 1753977834x7y5 − 7131900059x6y6 − 4268681790x5y7 + 73986295796x4y8 − 74922917352x3y9 − 197667466848x2y10 + 164683895040xy11 − 130767436800y12 : -43589145600y12) 1.1.1.1 13 view Hutz2026
13 (8354x13 + 48151x12y − 1206332x11y2 − 6298093x10y3 + 66314652x9y4 + 304427913x8y5 − 1745126036x7y6 − 6746939239x6y7 + 22669801274x5y8 + 67817345236x4y9 − 132792152232x3y10 − 235725166368x2y11 + 242569797120xy12 : 43589145600y13) 1.1.1.1 14 view Hutz2026
14 (34x14 − 5474x13y + 397033x12y2 − 17145856x11y3 + 490911421x10y4 − 9820782972x9y5 + 140949659279x8y6 − 1466929231768x7y7 + 11059905517661x6y8 − 59702976487154x5y9 + 225313258722188x4y10 − 570881108919576x3y11 + 907090218753984x2y12 − 796573394467200xy13 + 285901205990400y14 : 43589145600y14) 1.1.1.1 4 view DoHy2025
15 (41x15 − 7380x14y + 604100x13y2 − 29767920x12y3 + 985137062x11y4 − 23127063960x10y5 + 396533008300x9y6 − 5035984770960x8y7 + 47529555226153x7y8 − 331368195898740x6y9 + 1680182681686600x5y10 − 6029166612225120x4y11 + 14653631890929744x3y12 − 22451626097881920x2y13 + 19048387680000000xy14 − 6585448117248000y15 : 1307674368000y15) 1.1.1.1 7 view DoHy2025

Non-polynomial maps over ℚ Export to Sage

Degree Function Field of Definition Longest Tail Graph Citations
2 (264x2 + 291xy − 285y2 : -121x2 + 268xy + 285y2) 1.1.1.1 6 view BCHKW2014
3 (40x3 − 61x2y − 83xy2 + 90y3 : -40x3 + 15x2y − 5xy2 + 30y3) 1.1.1.1 8 view Hutz2026
4 (222x4 + 85x3y − 369x2y2 − 298xy3 − 60y4 : 4x4 + 258x3y + 93x2y2 − 185xy3 − 30y4) 1.1.1.1 9 view Hutz2026
6 (y6 : x6) 1.1.1.1 1 view dFH2018

Polynomials over quadratic fields Export to Sage

Degree Function Field of Definition Longest Tail Graph Citations
2 (x2 + (-1/2*a - 13/16)·y2 : y2) 2.2.17.1 4 view Doyle2014, Doyle2018
4 (x4 + y4 : y4) 2.0.3.1 1 view DoHi2025
6 (x6 + (a - 1)y6 : y6) 2.0.3.1 2 view DoHi2025

Postcritically Finite Maps Export to Sage

For each degree: whether the list is known to be complete, the number of conjugacy classes (over ℚ) in the database, and the sources of those maps. Its Export to Sage files contain all of the PCF maps counted in each row.

Polynomials over ℚ Export to Sage

Degree StatusClasses Citations
2 proven3 Morton1992, WR1994, FN1997, Poonen1998, Manes2008, Ingram2012, Doyle2014, Lukas2014, CV2017, Doyle2018, Doyle2020, DoHi2025
3 proven15 FN1997, Benedetto2009, Ingram2012, AMT2020
4 proven16 FN1997, GHJSX2021, Fraser2024
5 open1 FN1997
6 open1 FN1997
7 open1 FN1997
8 open1 FN1997
9 open1 FN1997
10 open1 FN1997

Non-polynomial maps over ℚ Export to Sage

Degree StatusClasses Citations
2 proven9* Lukas2014, CV2017, dFH2018, Vishkautsan2019, BS2026
3 open2* dFH2018, GHJSX2021
4 open1* dFH2018, GHJSX2021
5 open2* Miasnikov2017, dFH2018
6 open1* dFH2018
7 open1* dFH2018
11 open1* dFH2018

Polynomials over quadratic fields Export to Sage

Degree StatusClasses Citations
2 open1 Doyle2014, Doyle2018, Doyle2020
6 open1 DoHi2025

* Excludes polynomials, which are counted in the polynomial tables.

Small Canonical Heights Export to Sage

For each degree, the map with a rational point of the smallest known height ratio.

Polynomials over ℚ Export to Sage

Degree Function Field of Definition Point Height Ratio Citations
2 (x2 − 7xy − 12y2 : 6y2) 1.1.1.1 (0 : 1) 6.6042 · 10−3 BCHKW2014, Hutz2026
3 (2x3 + 21x2y + 25xy2 − 12y3 : -12y3) 1.1.1.1 (0 : 1) 9.2099 · 10−5 Benedetto2009, Hutz2026
4 (9x4 − 112x3y + 291x2y2 + 172xy3 + 120y4 : 120y4) 1.1.1.1 (0 : 1) 2.9015 · 10−6 Hutz2026
5 (x5 + 20x4y + 135x3y2 + 340x2y3 + 184xy4 + 40y5 : -40y5) 1.1.1.1 (0 : 1) 9.1519 · 10−9 Hutz2026
6 (29x6 + 639x5y + 4925x4y2 + 15345x3y3 + 12686x2y4 − 23544xy5 − 5040y6 : -5040y6) 1.1.1.1 (0 : 1) 1.8372 · 10−9 Hutz2026
7 (215x7 − 7601x6y + 100973x5y2 − 610445x4y3 + 1535960x3y4 − 546194x2y5 − 2468748xy6 + 166320y7 : -166320y7) 1.1.1.1 (0 : 1) 1.0564 · 10−10 Hutz2026
8 (55x8 + 1846x7y + 18550x6y2 + 15988x5y3 − 502775x4y4 − 21686x3y5 + 9132810x2y6 − 12969108xy7 − 2162160y8 : -2162160y8) 1.1.1.1 (0 : 1) 8.7710 · 10−13 Hutz2026
9 (2393x9 + 120789x8y + 2368272x7y2 + 22132656x6y3 + 91367367x5y4 + 43987671x4y5 − 669797792x3y6 − 974348316x2y7 + 1094978160xy8 − 129729600y9 : 129729600y9) 1.1.1.1 (0 : 1) 1.7173 · 10−14 Hutz2026
10 (947x10 − 64921x9y + 1852872x8y2 − 28455834x7y3 + 253612359x6y4 − 1317059289x5y5 + 3771140518x4y6 − 4957186196x3y7 − 134718696x2y8 + 8118980640xy9 − 518918400y10 : 518918400y10) 1.1.1.1 (0 : 1) 9.9368 · 10−16 Hutz2026
11 (141x11 + 9219x10y + 251060x9y2 + 3656820x8y3 + 30154233x7y4 + 133154847x6y5 + 223258230x5y6 − 332540670x4y7 − 1468215824x3y8 − 1620494616x2y9 − 1639499040xy10 − 518918400y11 : 518918400y11) 1.1.1.1 (0 : 1) 7.3446 · 10−17 Hutz2026
12 (1592279639x12 + 3158737074x11y − 642202438277x10y2 + 1327021417038x9y3 + 74225487274905x8y4 − 344961191466810x7y5 − 2329858471035263x6y6 + 16712209649304162x5y7 − 14142180837380044x4y8 − 57001311415764264x3y9 + 55257305950787040x2y10 − 27370257381331200xy11 + 9714712879872000y12 : 9714712879872000y12) 1.1.1.1 (0 : 1) 5.9715 · 10−19 Hutz2026

Non-polynomial maps over ℚ Export to Sage

Degree Function Field of Definition Point Height Ratio Citations
2 (592x2 − 3424xy + 1024y2 : 173x2 − 536xy − 1024y2) 1.1.1.1 (0 : 1) 4.6574 · 10−4 BCHKW2014, Hutz2026
3 (1115x3 − 2405x2y − 37855xy2 + 3465y3 : 201x3 + 173x2y + 1907xy2 − 3465y3) 1.1.1.1 (0 : 1) 3.0790 · 10−6 Hutz2026
4 (49x4 + 844x3y + 4499x2y2 + 7364xy3 − 660y4 : -10x4 − 174x3y − 866x2y2 − 1122xy3 + 660y4) 1.1.1.1 (0 : 1) 2.1843 · 10−8 Hutz2026
5 (88758966490337x5 + 2981527184876307x4y + 11066877636602289x3y2 − 75987409403569835x2y3 − 1288812439794810xy4 + 17419787236064304y5 : 1157006057963x5 − 50301712572351x4y − 1971337131131061x3y2 + 814941375750391x2y3 + 29505024045162162xy4 + 17419787236064304y5) 1.1.1.1 (0 : 1) 3.6941 · 10−10 Hutz2026
11 (x11 + 66x6y5 − 11xy10 : -11x10y − 66x5y6 + y11) 1.1.1.1 (-1 : 1) 1.0205 · 10−2 dFH2018

Automorphism Groups Export to Sage

For each automorphism group in the database, the map of smallest degree with exactly that group, and among those, the one over the smallest field. Groups are named as in GAP: Dn is dihedral of order 2n (D3 is written S3).

Group Order Degree Type Function Field of Definition Citations
C2 2 2 Polynomial (x2 : y2) 1.1.1.1 Morton1992, FN1997, Poonen1998, Manes2008, Ingram2012, Doyle2014, Lukas2014, Doyle2018, Doyle2020
C3 3 3 Non-polynomial (x3 − y3 : -x2y) 1.1.1.1 GHJSX2021
C2 × C2 4 3 Polynomial (x3 : y3) 1.1.1.1 FN1997, Ingram2012, AMT2020
C4 4 4 Non-polynomial (17xy3 : -4x4 − 4y4) 1.1.1.1 GHJSX2021
C5 5 6 Polynomial (x6 + xy5 : y6) 1.1.1.1 FN1997, dFH2018
C6 6 7 Polynomial (x7 + xy6 : y7) 1.1.1.1 FN1997, dFH2018
S3 6 2 Non-polynomial (y2 : x2) 1.1.1.1 Lukas2014, CV2017, dFH2018, BS2026
C7 7 8 Polynomial (x8 + xy7 : y8) 1.1.1.1 FN1997, dFH2018
C8 8 9 Polynomial (x9 + xy8 : y9) 1.1.1.1 FN1997, dFH2018
D4 8 3 Non-polynomial (y3 : x3) 1.1.1.1 dFH2018, GHJSX2021
C9 9 10 Polynomial (x10 + xy9 : y10) 1.1.1.1 FN1997
D5 10 4 Non-polynomial (y4 : x4) 1.1.1.1 dFH2018, GHJSX2021
A4 12 3 Non-polynomial (x3 − 3y3 : -3x2y) 1.1.1.1 GHJSX2021
D6 12 5 Non-polynomial (y5 : x5) 1.1.1.1 dFH2018
D7 14 6 Non-polynomial (y6 : x6) 1.1.1.1 dFH2018
D8 16 7 Non-polynomial (y7 : x7) 1.1.1.1 dFH2018
D9 18 10 Polynomial (x10 : y10) 1.1.1.1 FN1997
S4 24 5 Non-polynomial (x5 − 5xy4 : -5x4y + y5) 1.1.1.1 Miasnikov2017, dFH2018
A5 60 11 Non-polynomial (x11 + 66x6y5 − 11xy10 : -11x10y − 66x5y6 + y11) 1.1.1.1 dFH2018

Automorphism groups by degree

The nontrivial automorphism groups of the maps in the database, for each degree, polynomials and non-polynomial maps, over ℚ and over quadratic fields. Each group links to that degree's automorphism group page.

DegreeℚQuadratic fields
PolynomialNon-polynomialPolynomialNon-polynomial
2 C2C2, S3——
3 C2, C2 × C2C2, C3, C2 × C2, D4, A4——
4 C3, S3C2, C3, C4, S3, D5——
5 C2, C4, D4D6, S4——
6 C5, D5D7——
7 C2, C3, C6, D6D8——
8 C7, D7———
9 C2, C4, C8, D8———
10 C3, C9, D9———
11 —A5——