Triangle-maximal straight-line arrangements

Drag to pan, Ctrl+scroll to zoom, double-click to reset.

19 lines, base configuration

Satisfies the hypotheses of the Bartholdi–Blanc–Loisel iterative construction for the infinite series n = 18·2ᵗ+1.

19 lines, 107 triangles (upper bound 107)

0: y = 0 * x + 0
1: y = -0.18005569347392558 * x + -1.0211465809173328
2: y = -0.2523063234972156 * x + -0.2117101429902091
3: y = -0.3258394235197802 * x + -0.5643704366452125
4: y = -1.7452063993081608 * x + 4.794915174386878
5: y = -2.1794062523518547 * x + 0.38428812421435343
6: y = -2.79556530398616 * x + 3.331624994357231
7: y = -4.5958617573046405 * x + -5.4771347603341445
8: y = -5.672031403682503 * x + -0.0005672031403682503
9: y = -7.399054532171846 * x + -2.6930356114229927
10: y = -23.078923709484943 * x + 13.324622816277968
11: y = 4.390047176617791 * x + 12.061555488097895
12: y = 2.902043919920718 * x + 1.6754958383663434
13: y = 1.3184459031885964 * x + -0.4798750642508682
14: y = 0.9019247588148952 * x + -0.7568047324712357
15: y = 0.8450050393326853 * x + -0.00008450050393326853
16: y = 0.6406800735979308 * x + -1.1096904388685833
17: y = 0.4439270473162865 * x + 0.07827631590810467
18: y = 0.15548458427400286 * x + -0.8817968960239696
Line equations 
0: y = 0 * x + 0
1: y = -0.18005569347392558 * x + -1.0211465809173328
2: y = -0.2523063234972156 * x + -0.2117101429902091
3: y = -0.3258394235197802 * x + -0.5643704366452125
4: y = -1.7452063993081608 * x + 4.794915174386878
5: y = -2.1794062523518547 * x + 0.38428812421435343
6: y = -2.79556530398616 * x + 3.331624994357231
7: y = -4.5958617573046405 * x + -5.4771347603341445
8: y = -5.672031403682503 * x + -0.0005672031403682503
9: y = -7.399054532171846 * x + -2.6930356114229927
10: y = -23.078923709484943 * x + 13.324622816277968
11: y = 4.390047176617791 * x + 12.061555488097895
12: y = 2.902043919920718 * x + 1.6754958383663434
13: y = 1.3184459031885964 * x + -0.4798750642508682
14: y = 0.9019247588148952 * x + -0.7568047324712357
15: y = 0.8450050393326853 * x + -0.00008450050393326853
16: y = 0.6406800735979308 * x + -1.1096904388685833
17: y = 0.4439270473162865 * x + 0.07827631590810467
18: y = 0.15548458427400286 * x + -0.8817968960239696

37 lines, one-step from 19

First iterative step applied to the 19-line base configuration using the Bartholdi–Blanc–Loisel construction.

37 lines, 431 triangles (upper bound 431)

0: y = 0 * x + 0
1: y = -0.08525707453547601 * x + 0.9744928211209135
2: y = -0.2339858729432502 * x + 0.020471111307751623
3: y = -0.2483554366766241 * x + 0.9268751080131155
4: y = -0.37681666729948476 * x + 0.10096772169748398
5: y = -0.3896306275579346 * x + 0.8355655772404731
6: y = -0.4858050769234038 * x + 0.22653462773996136
7: y = -0.49044128961535655 * x + 0.7004227501882034
8: y = -0.5423677861583429 * x + 0.37977001235018354
9: y = -0.5459618226104826 * x + 0.5459618226104825
10: y = -8.328622559528835 * x + -47.233965704313775
11: y = -12.660815831961909 * x + -10.623685895002705
12: y = -14.47825312424336 * x + -25.077070016032323
13: y = -63.735129037270276 * x + 175.11082785592666
14: y = -76.69352198474006 * x + 13.523137171467495
15: y = -94.31492845913127 * x + 112.40015482643558
16: y = -126.53528611643902 * x + -150.79888181920248
17: y = -149.178780163709 * x + -0.014917878016370902
18: y = -181.35790128698025 * x + -66.008877817449
19: y = -328.6000398738666 * x + 189.71732147689863
20: y = 437.88436753411025 * x + 1203.0774121321363
21: y = 211.5348754768864 * x + 122.12971729957432
22: y = 76.38982118233967 * x + -27.803621111289477
23: y = 48.87567038161491 * x + -41.01155699075537
24: y = 45.59297099413981 * x + -0.004559297099413982
25: y = 33.34888152654313 * x + -57.76195717956782
26: y = 23.116860995340357 * x + 4.076126302765646
27: y = 7.502215170945896 * x + -42.547176505845606
28: y = 0.5417712358131785 * x + 0.5417712358131784
29: y = 0.5392477628885335 * x + 0.37758534853727327
30: y = 0.4880997944489145 * x + 0.6970787485334529
31: y = 0.481953142997064 * x + 0.22473844145140207
32: y = 0.38402576740064137 * x + 0.8235459158446695
33: y = 0.3747542934362467 * x + 0.10041511028633829
34: y = 0.2470088880787438 * x + 0.9218497202309656
35: y = 0.23316936691921122 * x + 0.020399676286947586
36: y = 0.08496850144146709 * x + 0.9711944155632218
Line equations 
0: y = 0 * x + 0
1: y = -0.08525707453547601 * x + 0.9744928211209135
2: y = -0.2339858729432502 * x + 0.020471111307751623
3: y = -0.2483554366766241 * x + 0.9268751080131155
4: y = -0.37681666729948476 * x + 0.10096772169748398
5: y = -0.3896306275579346 * x + 0.8355655772404731
6: y = -0.4858050769234038 * x + 0.22653462773996136
7: y = -0.49044128961535655 * x + 0.7004227501882034
8: y = -0.5423677861583429 * x + 0.37977001235018354
9: y = -0.5459618226104826 * x + 0.5459618226104825
10: y = -8.328622559528835 * x + -47.233965704313775
11: y = -12.660815831961909 * x + -10.623685895002705
12: y = -14.47825312424336 * x + -25.077070016032323
13: y = -63.735129037270276 * x + 175.11082785592666
14: y = -76.69352198474006 * x + 13.523137171467495
15: y = -94.31492845913127 * x + 112.40015482643558
16: y = -126.53528611643902 * x + -150.79888181920248
17: y = -149.178780163709 * x + -0.014917878016370902
18: y = -181.35790128698025 * x + -66.008877817449
19: y = -328.6000398738666 * x + 189.71732147689863
20: y = 437.88436753411025 * x + 1203.0774121321363
21: y = 211.5348754768864 * x + 122.12971729957432
22: y = 76.38982118233967 * x + -27.803621111289477
23: y = 48.87567038161491 * x + -41.01155699075537
24: y = 45.59297099413981 * x + -0.004559297099413982
25: y = 33.34888152654313 * x + -57.76195717956782
26: y = 23.116860995340357 * x + 4.076126302765646
27: y = 7.502215170945896 * x + -42.547176505845606
28: y = 0.5417712358131785 * x + 0.5417712358131784
29: y = 0.5392477628885335 * x + 0.37758534853727327
30: y = 0.4880997944489145 * x + 0.6970787485334529
31: y = 0.481953142997064 * x + 0.22473844145140207
32: y = 0.38402576740064137 * x + 0.8235459158446695
33: y = 0.3747542934362467 * x + 0.10041511028633829
34: y = 0.2470088880787438 * x + 0.9218497202309656
35: y = 0.23316936691921122 * x + 0.020399676286947586
36: y = 0.08496850144146709 * x + 0.9711944155632218

41 lines, one-step from 21

Single iterative step from a 21-line arrangement using the Forge–Ramírez Alfonsín construction. No infinite series is possible from the parent.

41 lines, 533 triangles (upper bound 533)

0: y = 19.6440380158708 * x + -0.578845642445838
1: y = 5.19983686759458 * x + 46.2669483580472
2: y = 2.97337242178767 * x + -0.255654502748468
3: y = 2.33409554657142 * x + 10.2073308592064
4: y = 2.03913847183038 * x + -0.634409531311398
5: y = 1.51939067684971 * x + 4.44408039396207
6: y = 1.14469295714126 * x + -0.383673607397969
7: y = 1.09198915528216 * x + 2.46780787838117
8: y = 0.947707289018028 * x + -0.581595297292468
9: y = 0.80896478221994 * x + 1.52592194561986
10: y = 0.708319546739286 * x + -0.46596899057913
11: y = 0.624766449916582 * x + 1.07709697251601
12: y = 0.592073396328359 * x + -0.522334544621754
13: y = 0.467419996326499 * x + 0.815211228257588
14: y = 0.364476352936825 * x + -0.358176891237224
15: y = 0.307097716326852 * x + 0.627325466449936
16: y = 0.252224697244642 * x + -0.606243665819936
17: y = 0.173239760811204 * x + 0.517542416022027
18: y = 0.125712170009275 * x + -0.500504814655953
19: y = 0.0567903240132735 * x + 0.473964134108348
20: y = 5.45339624351274e-18 * x + -0.747810827880863
21: y = -0.0566407268373554 * x + 0.474709003288992
22: y = -0.126026378587329 * x + -0.502668706579321
23: y = -0.173988094834067 * x + 0.520070556147547
24: y = -0.25426442214236 * x + -0.611448868231776
25: y = -0.309876980168933 * x + 0.632838712396089
26: y = -0.368480699536813 * x + -0.362861640209878
27: y = -0.474087518144302 * x + 0.826370333485319
28: y = -0.603198691333035 * x + -0.533094500199415
29: y = -0.636848012086688 * x + 1.09721398633079
30: y = -0.724090133958835 * x + -0.477608081683738
31: y = -0.829471506779334 * x + 1.56371844343208
32: y = -0.97587461794496 * x + -0.60078764216201
33: y = -1.12998251203546 * x + 2.55282240379824
34: y = -1.18598949150119 * x + -0.399745439534234
35: y = -1.59358094120356 * x + 4.65965510727435
36: y = -2.17751680508347 * x + -0.680853322380702
37: y = -2.51510426865305 * x + 10.9989476990021
38: y = -3.27532346737191 * x + -0.286935223516981
39: y = -6.19714088202275 * x + 55.1771409818031
40: y = -50.5023827311972 * x + -1.56858159736557
Line equations 
0: y = 19.6440380158708 * x + -0.578845642445838
1: y = 5.19983686759458 * x + 46.2669483580472
2: y = 2.97337242178767 * x + -0.255654502748468
3: y = 2.33409554657142 * x + 10.2073308592064
4: y = 2.03913847183038 * x + -0.634409531311398
5: y = 1.51939067684971 * x + 4.44408039396207
6: y = 1.14469295714126 * x + -0.383673607397969
7: y = 1.09198915528216 * x + 2.46780787838117
8: y = 0.947707289018028 * x + -0.581595297292468
9: y = 0.80896478221994 * x + 1.52592194561986
10: y = 0.708319546739286 * x + -0.46596899057913
11: y = 0.624766449916582 * x + 1.07709697251601
12: y = 0.592073396328359 * x + -0.522334544621754
13: y = 0.467419996326499 * x + 0.815211228257588
14: y = 0.364476352936825 * x + -0.358176891237224
15: y = 0.307097716326852 * x + 0.627325466449936
16: y = 0.252224697244642 * x + -0.606243665819936
17: y = 0.173239760811204 * x + 0.517542416022027
18: y = 0.125712170009275 * x + -0.500504814655953
19: y = 0.0567903240132735 * x + 0.473964134108348
20: y = 5.45339624351274e-18 * x + -0.747810827880863
21: y = -0.0566407268373554 * x + 0.474709003288992
22: y = -0.126026378587329 * x + -0.502668706579321
23: y = -0.173988094834067 * x + 0.520070556147547
24: y = -0.25426442214236 * x + -0.611448868231776
25: y = -0.309876980168933 * x + 0.632838712396089
26: y = -0.368480699536813 * x + -0.362861640209878
27: y = -0.474087518144302 * x + 0.826370333485319
28: y = -0.603198691333035 * x + -0.533094500199415
29: y = -0.636848012086688 * x + 1.09721398633079
30: y = -0.724090133958835 * x + -0.477608081683738
31: y = -0.829471506779334 * x + 1.56371844343208
32: y = -0.97587461794496 * x + -0.60078764216201
33: y = -1.12998251203546 * x + 2.55282240379824
34: y = -1.18598949150119 * x + -0.399745439534234
35: y = -1.59358094120356 * x + 4.65965510727435
36: y = -2.17751680508347 * x + -0.680853322380702
37: y = -2.51510426865305 * x + 10.9989476990021
38: y = -3.27532346737191 * x + -0.286935223516981
39: y = -6.19714088202275 * x + 55.1771409818031
40: y = -50.5023827311972 * x + -1.56858159736557

45 lines, one-step from 23

Single iterative step from a 23-line arrangement using the Forge–Ramírez Alfonsín construction. No infinite series is possible from the parent.

45 lines, 645 triangles (upper bound 645)

0: y = 1.53430417945565 * x + 0.20403146857486
1: y = -0.519717793360893 * x + -1.0123770007636
2: y = 1.22463734160685 * x + 0.361302797408153
3: y = -0.682592554218052 * x + -1.18681219034012
4: y = 0.891854978259324 * x + 0.316083666124596
5: y = -0.870047509959627 * x + -1.47843485760808
6: y = 0.651476460231005 * x + 0.418124154690683
7: y = -1.09636719038685 * x + -1.97015219221493
8: y = 0.396929305083391 * x + 0.286795175281954
9: y = -1.41989120786806 * x + -2.83983360068664
10: y = 0.272556432493848 * x + 0.499073931073725
11: y = -1.87010286558218 * x + -4.37575147679071
12: y = 0.108540530144518 * x + 0.413263071246813
13: y = -2.5103136907933 * x + -7.37929773678778
14: y = 0 * x + 0.610545074014735
15: y = -3.52443245742084 * x + -15.0932528519642
16: y = -0.15596198360546 * x + 0.355345732571265
17: y = -7.25076505035506 * x + -63.4720982341358
18: y = -0.274318853521862 * x + 0.389406637042344
19: y = -0.393772372893695 * x + 0.27252089035818
20: y = 6.11597424517132 * x + -61.5713675655963
21: y = -0.584242811465604 * x + 0.433463267312579
22: y = 2.99158206439091 * x + -15.7352961692028
23: y = -0.724111708173206 * x + 0.181281981043461
24: y = 1.96411862253783 * x + -7.32581355453173
25: y = -1.08905653302851 * x + 0.461023808411459
26: y = 1.37117853979795 * x + -4.18294030008071
27: y = -1.29134149027236 * x + 0.418287739507626
28: y = 0.993450056980779 * x + -2.69385966502562
29: y = -1.74197588871076 * x + 0.717639658599045
30: y = 0.746886415976471 * x + -1.9669652534109
31: y = -1.89849013127593 * x + 0.349476299783515
32: y = 0.538492493879797 * x + -1.52059345557914
33: y = -2.7586087357052 * x + 0.658112245930578
34: y = 0.351699573604613 * x + -1.23335298576353
35: y = -3.91743259598345 * x + -0.0661110689538446
36: y = 0.170375461501831 * x + -1.03320644694924
37: y = -47.3722474445319 * x + 1.43579772315994
38: y = 0.0203941950811925 * x + -0.914576078806777
39: y = 29.6728308554765 * x + 1.4775805773327
40: y = -0.104237468278218 * x + -0.868327950312221
41: y = 3.68039533050188 * x + -0.083492590289976
42: y = -0.237082763091935 * x + -0.868846495493857
43: y = 2.41186113356395 * x + 0.327174404614809
44: y = -0.37333249578809 * x + -0.912399480160171
Line equations 
0: y = 1.53430417945565 * x + 0.20403146857486
1: y = -0.519717793360893 * x + -1.0123770007636
2: y = 1.22463734160685 * x + 0.361302797408153
3: y = -0.682592554218052 * x + -1.18681219034012
4: y = 0.891854978259324 * x + 0.316083666124596
5: y = -0.870047509959627 * x + -1.47843485760808
6: y = 0.651476460231005 * x + 0.418124154690683
7: y = -1.09636719038685 * x + -1.97015219221493
8: y = 0.396929305083391 * x + 0.286795175281954
9: y = -1.41989120786806 * x + -2.83983360068664
10: y = 0.272556432493848 * x + 0.499073931073725
11: y = -1.87010286558218 * x + -4.37575147679071
12: y = 0.108540530144518 * x + 0.413263071246813
13: y = -2.5103136907933 * x + -7.37929773678778
14: y = 0 * x + 0.610545074014735
15: y = -3.52443245742084 * x + -15.0932528519642
16: y = -0.15596198360546 * x + 0.355345732571265
17: y = -7.25076505035506 * x + -63.4720982341358
18: y = -0.274318853521862 * x + 0.389406637042344
19: y = -0.393772372893695 * x + 0.27252089035818
20: y = 6.11597424517132 * x + -61.5713675655963
21: y = -0.584242811465604 * x + 0.433463267312579
22: y = 2.99158206439091 * x + -15.7352961692028
23: y = -0.724111708173206 * x + 0.181281981043461
24: y = 1.96411862253783 * x + -7.32581355453173
25: y = -1.08905653302851 * x + 0.461023808411459
26: y = 1.37117853979795 * x + -4.18294030008071
27: y = -1.29134149027236 * x + 0.418287739507626
28: y = 0.993450056980779 * x + -2.69385966502562
29: y = -1.74197588871076 * x + 0.717639658599045
30: y = 0.746886415976471 * x + -1.9669652534109
31: y = -1.89849013127593 * x + 0.349476299783515
32: y = 0.538492493879797 * x + -1.52059345557914
33: y = -2.7586087357052 * x + 0.658112245930578
34: y = 0.351699573604613 * x + -1.23335298576353
35: y = -3.91743259598345 * x + -0.0661110689538446
36: y = 0.170375461501831 * x + -1.03320644694924
37: y = -47.3722474445319 * x + 1.43579772315994
38: y = 0.0203941950811925 * x + -0.914576078806777
39: y = 29.6728308554765 * x + 1.4775805773327
40: y = -0.104237468278218 * x + -0.868327950312221
41: y = 3.68039533050188 * x + -0.083492590289976
42: y = -0.237082763091935 * x + -0.868846495493857
43: y = 2.41186113356395 * x + 0.327174404614809
44: y = -0.37333249578809 * x + -0.912399480160171

25 lines, pentagonal defect

An arrangement of 25 straight lines with a pentagonal defect (190 affine triangles, upper bound 191). Adding the line at infinity gives 26 projective lines attaining the projective upper bound (n(n−1)−5)/3 = 215. No infinite series is possible from the parent.

25 lines, 190 triangles (upper bound 191)

0: y = -46.0555689553068 * x + -1.46531821729453
1: y = -5.18628226773342 * x + -0.750889674228041
2: y = -3.79690170872692 * x + 0.0858776775928565
3: y = -2.85344506534231 * x + -0.0830288031539976
4: y = -2.22081316083675 * x + 0.682170115254577
5: y = -1.39166330107018 * x + 0.161009614983008
6: y = -1.19665691201848 * x + 0.215556059240826
7: y = -0.995446060522662 * x + 0.116777793873404
8: y = -0.877592277490292 * x + 0.246872628793352
9: y = -0.66117002645792 * x + 0.164998514318484
10: y = -0.353507834151929 * x + 0.238515911596996
11: y = -0.258712565001472 * x + 0.189667686437379
12: y = -0.178593719264751 * x + 0.261208646885366
13: y = 6.72087096676665e-17 * x + 0.217830462424964
14: y = 0.282529163641343 * x + 0.271463460849496
15: y = 0.369037104441885 * x + 0.224602681173834
16: y = 0.560600607545068 * x + 0.311019004004647
17: y = 0.729147946955818 * x + 0.220328202868728
18: y = 1.08724832025342 * x + 0.326233494832119
19: y = 1.30735445184197 * x + 0.231207070325775
20: y = 1.72355125510505 * x + 0.334927373436534
21: y = 2.54708768133625 * x + 0.184600572522407
22: y = 4.45341098936655 * x + 0.471542049005592
23: y = 6.57618564403709 * x + -0.0820831930796701
24: y = 129.654799521792 * x + 7.64905716235248
Line equations 
0: y = -46.0555689553068 * x + -1.46531821729453
1: y = -5.18628226773342 * x + -0.750889674228041
2: y = -3.79690170872692 * x + 0.0858776775928565
3: y = -2.85344506534231 * x + -0.0830288031539976
4: y = -2.22081316083675 * x + 0.682170115254577
5: y = -1.39166330107018 * x + 0.161009614983008
6: y = -1.19665691201848 * x + 0.215556059240826
7: y = -0.995446060522662 * x + 0.116777793873404
8: y = -0.877592277490292 * x + 0.246872628793352
9: y = -0.66117002645792 * x + 0.164998514318484
10: y = -0.353507834151929 * x + 0.238515911596996
11: y = -0.258712565001472 * x + 0.189667686437379
12: y = -0.178593719264751 * x + 0.261208646885366
13: y = 6.72087096676665e-17 * x + 0.217830462424964
14: y = 0.282529163641343 * x + 0.271463460849496
15: y = 0.369037104441885 * x + 0.224602681173834
16: y = 0.560600607545068 * x + 0.311019004004647
17: y = 0.729147946955818 * x + 0.220328202868728
18: y = 1.08724832025342 * x + 0.326233494832119
19: y = 1.30735445184197 * x + 0.231207070325775
20: y = 1.72355125510505 * x + 0.334927373436534
21: y = 2.54708768133625 * x + 0.184600572522407
22: y = 4.45341098936655 * x + 0.471542049005592
23: y = 6.57618564403709 * x + -0.0820831930796701
24: y = 129.654799521792 * x + 7.64905716235248

49 lines, one-step from 25, pentagonal defect

One iterative step from the 25-line pentagonal-defect arrangement using the Forge–Ramírez Alfonsín construction. Adding the line at infinity gives 50 projective lines attaining the projective upper bound (n(n−1)−5)/3 = 815. No infinite series is possible from the parent.

49 lines, 766 triangles (upper bound 767)

0: y = 6.72087096676665e-17 * x + 0.217830462424964
1: y = -1.38633874004363 * x + -4.26740895121216
2: y = -0.178593719264751 * x + 0.261208646885366
3: y = -1.74557647243754 * x + -5.80616944559249
4: y = -0.258712565001472 * x + 0.189667686437379
5: y = -2.24285293310251 * x + -8.66040672100139
6: y = -0.353507834151929 * x + 0.238515911596996
7: y = -3.10922331562523 * x + -15.3818541820559
8: y = -0.66117002645792 * x + 0.164998514318484
9: y = -4.83299481243358 * x + -35.0995582335726
10: y = -0.877592277490292 * x + 0.246872628793352
11: y = -9.31172121477317 * x + -131.426979526286
12: y = -0.995446060522662 * x + 0.116777793873404
13: y = -1.19665691201848 * x + 0.215556059240826
14: y = 12.5800836924087 * x + -176.839931627479
15: y = -1.39166330107018 * x + 0.161009614983008
16: y = 5.49456263786724 * x + -39.8341106850988
17: y = -2.22081316083675 * x + 0.682170115254577
18: y = 3.20278128285964 * x + -16.4727277722362
19: y = -2.85344506534231 * x + -0.0830288031539976
20: y = 2.20717946036131 * x + -9.17002987059495
21: y = -3.79690170872692 * x + 0.0858776775928565
22: y = 1.63848450326812 * x + -6.04728114050171
23: y = -5.18628226773342 * x + -0.750889674228041
24: y = 1.24442040185838 * x + -4.38003995828891
25: y = -46.0555689553068 * x + -1.46531821729453
26: y = 0.92431390791712 * x + -3.35613355966111
27: y = 129.654799521792 * x + 7.64905716235248
28: y = 0.684362668659003 * x + -2.75226570530167
29: y = 6.57618564403709 * x + -0.0820831930796701
30: y = 0.472092528597347 * x + -2.35852938361564
31: y = 4.45341098936655 * x + 0.471542049005592
32: y = 0.28686200849897 * x + -2.10161461122388
33: y = 2.54708768133625 * x + 0.184600572522407
34: y = 0.123265385421044 * x + -1.95952550152771
35: y = 1.72355125510505 * x + 0.334927373436534
36: y = -0.0270981435530029 * x + -1.90629756733898
37: y = 1.30735445184197 * x + 0.231207070325775
38: y = -0.183926366054319 * x + -1.91359028863284
39: y = 1.08724832025342 * x + 0.326233494832119
40: y = -0.342016231869149 * x + -1.98245375299348
41: y = 0.729147946955818 * x + 0.220328202868728
42: y = -0.504978495468646 * x + -2.12679292469043
43: y = 0.560600607545068 * x + 0.311019004004647
44: y = -0.682154266749916 * x + -2.38118358853226
45: y = 0.369037104441885 * x + 0.224602681173834
46: y = -0.88130945062193 * x + -2.76556081275289
47: y = 0.282529163641343 * x + 0.271463460849496
48: y = -1.11022806382526 * x + -3.33597933384463
Line equations 
0: y = 6.72087096676665e-17 * x + 0.217830462424964
1: y = -1.38633874004363 * x + -4.26740895121216
2: y = -0.178593719264751 * x + 0.261208646885366
3: y = -1.74557647243754 * x + -5.80616944559249
4: y = -0.258712565001472 * x + 0.189667686437379
5: y = -2.24285293310251 * x + -8.66040672100139
6: y = -0.353507834151929 * x + 0.238515911596996
7: y = -3.10922331562523 * x + -15.3818541820559
8: y = -0.66117002645792 * x + 0.164998514318484
9: y = -4.83299481243358 * x + -35.0995582335726
10: y = -0.877592277490292 * x + 0.246872628793352
11: y = -9.31172121477317 * x + -131.426979526286
12: y = -0.995446060522662 * x + 0.116777793873404
13: y = -1.19665691201848 * x + 0.215556059240826
14: y = 12.5800836924087 * x + -176.839931627479
15: y = -1.39166330107018 * x + 0.161009614983008
16: y = 5.49456263786724 * x + -39.8341106850988
17: y = -2.22081316083675 * x + 0.682170115254577
18: y = 3.20278128285964 * x + -16.4727277722362
19: y = -2.85344506534231 * x + -0.0830288031539976
20: y = 2.20717946036131 * x + -9.17002987059495
21: y = -3.79690170872692 * x + 0.0858776775928565
22: y = 1.63848450326812 * x + -6.04728114050171
23: y = -5.18628226773342 * x + -0.750889674228041
24: y = 1.24442040185838 * x + -4.38003995828891
25: y = -46.0555689553068 * x + -1.46531821729453
26: y = 0.92431390791712 * x + -3.35613355966111
27: y = 129.654799521792 * x + 7.64905716235248
28: y = 0.684362668659003 * x + -2.75226570530167
29: y = 6.57618564403709 * x + -0.0820831930796701
30: y = 0.472092528597347 * x + -2.35852938361564
31: y = 4.45341098936655 * x + 0.471542049005592
32: y = 0.28686200849897 * x + -2.10161461122388
33: y = 2.54708768133625 * x + 0.184600572522407
34: y = 0.123265385421044 * x + -1.95952550152771
35: y = 1.72355125510505 * x + 0.334927373436534
36: y = -0.0270981435530029 * x + -1.90629756733898
37: y = 1.30735445184197 * x + 0.231207070325775
38: y = -0.183926366054319 * x + -1.91359028863284
39: y = 1.08724832025342 * x + 0.326233494832119
40: y = -0.342016231869149 * x + -1.98245375299348
41: y = 0.729147946955818 * x + 0.220328202868728
42: y = -0.504978495468646 * x + -2.12679292469043
43: y = 0.560600607545068 * x + 0.311019004004647
44: y = -0.682154266749916 * x + -2.38118358853226
45: y = 0.369037104441885 * x + 0.224602681173834
46: y = -0.88130945062193 * x + -2.76556081275289
47: y = 0.282529163641343 * x + 0.271463460849496
48: y = -1.11022806382526 * x + -3.33597933384463

38 lines, one line added to 37

Obtained by adding one line to the 37-line configuration. Does not attain the upper bound but provides a lower bound for n = 38.

38 lines, 448 triangles (upper bound 451)

0: y = 8.5 * x + 420
1: y = -0.0511491135982793 * x + -0.9178785309184401
2: y = -0.11428557227883823 * x + 1.3107393606160445
3: y = -0.19118397445931906 * x + -0.8057004322548322
4: y = -0.25225668665803613 * x + 1.2801279021381529
5: y = -0.3287340648743173 * x + -0.5683693916196748
6: y = -0.35729789323707967 * x + 1.1263416669721444
7: y = -0.4356486765449741 * x + -0.2582163170338081
8: y = -0.4486005395283 * x + 0.7997569089166494
9: y = -0.48452581528055966 * x + 0.07286939212967697
10: y = -0.49722737423645175 * x + 0.42908157009969744
11: y = -1.8208326874917304 * x + -23.849953906460513
12: y = -2.668759725903984 * x + -4.455534873089999
13: y = -3.077717216212927 * x + -11.29523871383243
14: y = -13.46382544885264 * x + 128.61064074691464
15: y = -28.681903737976807 * x + 29.992711133704955
16: y = -45.73309907166091 * x + 158.04683300437003
17: y = -195.7918363468965 * x + -535.2508887565817
18: y = 152.01448008098333 * x + -42.44899868017251
19: y = 76.05661550019619 * x + 40.67250885939267
20: y = 38.182124225316436 * x + -79.67881870212177
21: y = 17.144754676948857 * x + 96.47014435972454
22: y = 13.247787651082444 * x + 13.555605276467427
23: y = 8.332159286564195 * x + -12.433114865924969
24: y = 6.507492375820513 * x + -16.802709144639223
25: y = 5.912939652272375 * x + -3.668777005687785
26: y = 4.878997184047106 * x + -24.314733210222663
27: y = 3.6406429401031404 * x + 0.6201187476770453
28: y = 0.9834742758544991 * x + -18.42215151694215
29: y = 0.4250392014668045 * x + 0.06986636649553882
30: y = 0.4144576107070151 * x + -0.3086003410578292
31: y = 0.39666874638809896 * x + 0.4275159431457279
32: y = 0.3553175727243024 * x + -0.5868027185305132
33: y = 0.3235159138797628 * x + 0.7374202113945163
34: y = 0.25910129467476045 * x + -0.7778379577181133
35: y = 0.20641814226447244 * x + 1.0227856773121415
36: y = 0.0908914152206821 * x + -0.9118628440891252
37: y = 0.05724425445170875 * x + 1.2174876030436963
Line equations 
0: y = 8.5 * x + 420
1: y = -0.0511491135982793 * x + -0.9178785309184401
2: y = -0.11428557227883823 * x + 1.3107393606160445
3: y = -0.19118397445931906 * x + -0.8057004322548322
4: y = -0.25225668665803613 * x + 1.2801279021381529
5: y = -0.3287340648743173 * x + -0.5683693916196748
6: y = -0.35729789323707967 * x + 1.1263416669721444
7: y = -0.4356486765449741 * x + -0.2582163170338081
8: y = -0.4486005395283 * x + 0.7997569089166494
9: y = -0.48452581528055966 * x + 0.07286939212967697
10: y = -0.49722737423645175 * x + 0.42908157009969744
11: y = -1.8208326874917304 * x + -23.849953906460513
12: y = -2.668759725903984 * x + -4.455534873089999
13: y = -3.077717216212927 * x + -11.29523871383243
14: y = -13.46382544885264 * x + 128.61064074691464
15: y = -28.681903737976807 * x + 29.992711133704955
16: y = -45.73309907166091 * x + 158.04683300437003
17: y = -195.7918363468965 * x + -535.2508887565817
18: y = 152.01448008098333 * x + -42.44899868017251
19: y = 76.05661550019619 * x + 40.67250885939267
20: y = 38.182124225316436 * x + -79.67881870212177
21: y = 17.144754676948857 * x + 96.47014435972454
22: y = 13.247787651082444 * x + 13.555605276467427
23: y = 8.332159286564195 * x + -12.433114865924969
24: y = 6.507492375820513 * x + -16.802709144639223
25: y = 5.912939652272375 * x + -3.668777005687785
26: y = 4.878997184047106 * x + -24.314733210222663
27: y = 3.6406429401031404 * x + 0.6201187476770453
28: y = 0.9834742758544991 * x + -18.42215151694215
29: y = 0.4250392014668045 * x + 0.06986636649553882
30: y = 0.4144576107070151 * x + -0.3086003410578292
31: y = 0.39666874638809896 * x + 0.4275159431457279
32: y = 0.3553175727243024 * x + -0.5868027185305132
33: y = 0.3235159138797628 * x + 0.7374202113945163
34: y = 0.25910129467476045 * x + -0.7778379577181133
35: y = 0.20641814226447244 * x + 1.0227856773121415
36: y = 0.0908914152206821 * x + -0.9118628440891252
37: y = 0.05724425445170875 * x + 1.2174876030436963

42 lines, one line added to 41

Obtained by adding one line to the 41-line configuration. Does not attain the upper bound but provides a lower bound for n = 42.

42 lines, 553 triangles (upper bound 555)

0: y = 0 * x + 70
1: y = 19.6440380158708 * x + -0.578845642445838
2: y = 5.19983686759458 * x + 46.2669483580472
3: y = 2.97337242178767 * x + -0.255654502748468
4: y = 2.33409554657142 * x + 10.2073308592064
5: y = 2.03913847183038 * x + -0.634409531311398
6: y = 1.51939067684971 * x + 4.44408039396207
7: y = 1.14469295714126 * x + -0.383673607397969
8: y = 1.09198915528216 * x + 2.46780787838117
9: y = 0.947707289018028 * x + -0.581595297292468
10: y = 0.80896478221994 * x + 1.52592194561986
11: y = 0.708319546739286 * x + -0.46596899057913
12: y = 0.624766449916582 * x + 1.07709697251601
13: y = 0.592073396328359 * x + -0.522334544621754
14: y = 0.467419996326499 * x + 0.815211228257588
15: y = 0.364476352936825 * x + -0.358176891237224
16: y = 0.307097716326852 * x + 0.627325466449936
17: y = 0.252224697244642 * x + -0.606243665819936
18: y = 0.173239760811204 * x + 0.517542416022027
19: y = 0.125712170009275 * x + -0.500504814655953
20: y = 0.0567903240132735 * x + 0.473964134108348
21: y = 5.45339624351274e-18 * x + -0.747810827880863
22: y = -0.0566407268373554 * x + 0.474709003288992
23: y = -0.126026378587329 * x + -0.502668706579321
24: y = -0.173988094834067 * x + 0.520070556147547
25: y = -0.25426442214236 * x + -0.611448868231776
26: y = -0.309876980168933 * x + 0.632838712396089
27: y = -0.368480699536813 * x + -0.362861640209878
28: y = -0.474087518144302 * x + 0.826370333485319
29: y = -0.603198691333035 * x + -0.533094500199415
30: y = -0.636848012086688 * x + 1.09721398633079
31: y = -0.724090133958835 * x + -0.477608081683738
32: y = -0.829471506779334 * x + 1.56371844343208
33: y = -0.97587461794496 * x + -0.60078764216201
34: y = -1.12998251203546 * x + 2.55282240379824
35: y = -1.18598949150119 * x + -0.399745439534234
36: y = -1.59358094120356 * x + 4.65965510727435
37: y = -2.17751680508347 * x + -0.680853322380702
38: y = -2.51510426865305 * x + 10.9989476990021
39: y = -3.27532346737191 * x + -0.286935223516981
40: y = -6.19714088202275 * x + 55.1771409818031
41: y = -50.5023827311972 * x + -1.56858159736557
Line equations 
0: y = 0 * x + 70
1: y = 19.6440380158708 * x + -0.578845642445838
2: y = 5.19983686759458 * x + 46.2669483580472
3: y = 2.97337242178767 * x + -0.255654502748468
4: y = 2.33409554657142 * x + 10.2073308592064
5: y = 2.03913847183038 * x + -0.634409531311398
6: y = 1.51939067684971 * x + 4.44408039396207
7: y = 1.14469295714126 * x + -0.383673607397969
8: y = 1.09198915528216 * x + 2.46780787838117
9: y = 0.947707289018028 * x + -0.581595297292468
10: y = 0.80896478221994 * x + 1.52592194561986
11: y = 0.708319546739286 * x + -0.46596899057913
12: y = 0.624766449916582 * x + 1.07709697251601
13: y = 0.592073396328359 * x + -0.522334544621754
14: y = 0.467419996326499 * x + 0.815211228257588
15: y = 0.364476352936825 * x + -0.358176891237224
16: y = 0.307097716326852 * x + 0.627325466449936
17: y = 0.252224697244642 * x + -0.606243665819936
18: y = 0.173239760811204 * x + 0.517542416022027
19: y = 0.125712170009275 * x + -0.500504814655953
20: y = 0.0567903240132735 * x + 0.473964134108348
21: y = 5.45339624351274e-18 * x + -0.747810827880863
22: y = -0.0566407268373554 * x + 0.474709003288992
23: y = -0.126026378587329 * x + -0.502668706579321
24: y = -0.173988094834067 * x + 0.520070556147547
25: y = -0.25426442214236 * x + -0.611448868231776
26: y = -0.309876980168933 * x + 0.632838712396089
27: y = -0.368480699536813 * x + -0.362861640209878
28: y = -0.474087518144302 * x + 0.826370333485319
29: y = -0.603198691333035 * x + -0.533094500199415
30: y = -0.636848012086688 * x + 1.09721398633079
31: y = -0.724090133958835 * x + -0.477608081683738
32: y = -0.829471506779334 * x + 1.56371844343208
33: y = -0.97587461794496 * x + -0.60078764216201
34: y = -1.12998251203546 * x + 2.55282240379824
35: y = -1.18598949150119 * x + -0.399745439534234
36: y = -1.59358094120356 * x + 4.65965510727435
37: y = -2.17751680508347 * x + -0.680853322380702
38: y = -2.51510426865305 * x + 10.9989476990021
39: y = -3.27532346737191 * x + -0.286935223516981
40: y = -6.19714088202275 * x + 55.1771409818031
41: y = -50.5023827311972 * x + -1.56858159736557

46 lines, one line added to 45

Obtained by adding one line to the 45-line configuration. Does not attain the upper bound but provides a lower bound for n = 46.

46 lines, 667 triangles (upper bound 669)

0: y = 0 * x + -400
1: y = 1.53430417945565 * x + 0.20403146857486
2: y = -0.519717793360893 * x + -1.0123770007636
3: y = 1.22463734160685 * x + 0.361302797408153
4: y = -0.682592554218052 * x + -1.18681219034012
5: y = 0.891854978259324 * x + 0.316083666124596
6: y = -0.870047509959627 * x + -1.47843485760808
7: y = 0.651476460231005 * x + 0.418124154690683
8: y = -1.09636719038685 * x + -1.97015219221493
9: y = 0.396929305083391 * x + 0.286795175281954
10: y = -1.41989120786806 * x + -2.83983360068664
11: y = 0.272556432493848 * x + 0.499073931073725
12: y = -1.87010286558218 * x + -4.37575147679071
13: y = 0.108540530144518 * x + 0.413263071246813
14: y = -2.5103136907933 * x + -7.37929773678778
15: y = 0 * x + 0.610545074014735
16: y = -3.52443245742084 * x + -15.0932528519642
17: y = -0.15596198360546 * x + 0.355345732571265
18: y = -7.25076505035506 * x + -63.4720982341358
19: y = -0.274318853521862 * x + 0.389406637042344
20: y = -0.393772372893695 * x + 0.27252089035818
21: y = 6.11597424517132 * x + -61.5713675655963
22: y = -0.584242811465604 * x + 0.433463267312579
23: y = 2.99158206439091 * x + -15.7352961692028
24: y = -0.724111708173206 * x + 0.181281981043461
25: y = 1.96411862253783 * x + -7.32581355453173
26: y = -1.08905653302851 * x + 0.461023808411459
27: y = 1.37117853979795 * x + -4.18294030008071
28: y = -1.29134149027236 * x + 0.418287739507626
29: y = 0.993450056980779 * x + -2.69385966502562
30: y = -1.74197588871076 * x + 0.717639658599045
31: y = 0.746886415976471 * x + -1.9669652534109
32: y = -1.89849013127593 * x + 0.349476299783515
33: y = 0.538492493879797 * x + -1.52059345557914
34: y = -2.7586087357052 * x + 0.658112245930578
35: y = 0.351699573604613 * x + -1.23335298576353
36: y = -3.91743259598345 * x + -0.0661110689538446
37: y = 0.170375461501831 * x + -1.03320644694924
38: y = -47.3722474445319 * x + 1.43579772315994
39: y = 0.0203941950811925 * x + -0.914576078806777
40: y = 29.6728308554765 * x + 1.4775805773327
41: y = -0.104237468278218 * x + -0.868327950312221
42: y = 3.68039533050188 * x + -0.083492590289976
43: y = -0.237082763091935 * x + -0.868846495493857
44: y = 2.41186113356395 * x + 0.327174404614809
45: y = -0.37333249578809 * x + -0.912399480160171
Line equations 
0: y = 0 * x + -400
1: y = 1.53430417945565 * x + 0.20403146857486
2: y = -0.519717793360893 * x + -1.0123770007636
3: y = 1.22463734160685 * x + 0.361302797408153
4: y = -0.682592554218052 * x + -1.18681219034012
5: y = 0.891854978259324 * x + 0.316083666124596
6: y = -0.870047509959627 * x + -1.47843485760808
7: y = 0.651476460231005 * x + 0.418124154690683
8: y = -1.09636719038685 * x + -1.97015219221493
9: y = 0.396929305083391 * x + 0.286795175281954
10: y = -1.41989120786806 * x + -2.83983360068664
11: y = 0.272556432493848 * x + 0.499073931073725
12: y = -1.87010286558218 * x + -4.37575147679071
13: y = 0.108540530144518 * x + 0.413263071246813
14: y = -2.5103136907933 * x + -7.37929773678778
15: y = 0 * x + 0.610545074014735
16: y = -3.52443245742084 * x + -15.0932528519642
17: y = -0.15596198360546 * x + 0.355345732571265
18: y = -7.25076505035506 * x + -63.4720982341358
19: y = -0.274318853521862 * x + 0.389406637042344
20: y = -0.393772372893695 * x + 0.27252089035818
21: y = 6.11597424517132 * x + -61.5713675655963
22: y = -0.584242811465604 * x + 0.433463267312579
23: y = 2.99158206439091 * x + -15.7352961692028
24: y = -0.724111708173206 * x + 0.181281981043461
25: y = 1.96411862253783 * x + -7.32581355453173
26: y = -1.08905653302851 * x + 0.461023808411459
27: y = 1.37117853979795 * x + -4.18294030008071
28: y = -1.29134149027236 * x + 0.418287739507626
29: y = 0.993450056980779 * x + -2.69385966502562
30: y = -1.74197588871076 * x + 0.717639658599045
31: y = 0.746886415976471 * x + -1.9669652534109
32: y = -1.89849013127593 * x + 0.349476299783515
33: y = 0.538492493879797 * x + -1.52059345557914
34: y = -2.7586087357052 * x + 0.658112245930578
35: y = 0.351699573604613 * x + -1.23335298576353
36: y = -3.91743259598345 * x + -0.0661110689538446
37: y = 0.170375461501831 * x + -1.03320644694924
38: y = -47.3722474445319 * x + 1.43579772315994
39: y = 0.0203941950811925 * x + -0.914576078806777
40: y = 29.6728308554765 * x + 1.4775805773327
41: y = -0.104237468278218 * x + -0.868327950312221
42: y = 3.68039533050188 * x + -0.083492590289976
43: y = -0.237082763091935 * x + -0.868846495493857
44: y = 2.41186113356395 * x + 0.327174404614809
45: y = -0.37333249578809 * x + -0.912399480160171