Al Zimmermann’s Programming Contests
Polyhedra — Final Report

Congratulations to Pascal Zimmer for finishing at the top in the Polyhedra Programming Contest -- he wins US$500 for his efforts. Congratulations also go to Giorgio Di Falco and Ivan Kazmenko for finishing second and third, respectively - their prizes are US$100 and a copy of Cabri Geometry II Plus (donated by Cabriolog).

Here are the final standings:

Rank Score Entrant Areas
45678910111213141516171819202122232425262728
124.991Pascal Zimmer
Nice, France
16.55839.96277.852136.498220.155350.606490.401679.515895.5641193.3171501.5921883.2842318.3622861.1683437.4914101.9094830.1745692.1286615.3997640.5078759.3289981.26011317.94212748.50814334.688
224.856Giorgio Di Falco
Rome, Italy
16.55839.96277.852136.498219.978333.784478.610661.896890.0971171.9991485.4771889.9782318.3622861.1683435.2064120.1784830.5535692.1286596.2007642.8728756.0249960.09011287.55212745.46814320.496
324.835Ivan Kazmenko
Saint-Petersburg, Russia
16.55839.96277.852136.498220.155334.200479.132662.260890.0971171.9991485.4771889.9782318.3622861.1683417.0924120.1784826.5015698.0766572.0147642.8728694.3029981.26011237.41312748.50814225.455
424.822Jim Gillogly
Westwood, California, United States
16.55839.96277.852136.498220.155334.197479.132663.926890.0971171.9991485.4771889.9782318.3622859.9673435.2064101.9094828.8435692.1286613.9257620.9338708.1649915.62511207.07312649.85514177.677
524.821Mark Beyleveld
Sugar Land, Texas, United States
16.55839.96277.852136.498220.155334.197479.132663.926890.0971171.9991485.4771889.9782312.9222859.9673411.2504120.1784817.7455698.0766558.0107640.5078675.1579981.26011211.30912739.43014192.013
624.815Gabriel Pîrvan
Rîmnicu Sarat, Romania
16.55839.96277.852136.498220.155334.200479.132663.926890.0971171.9991489.8431883.2842318.3622859.9673417.0924101.9094826.5015692.1286562.0187607.5078694.3029960.09011212.34312694.59614216.306
724.809Jaroslaw Wroblewski
Wroclaw, Poland
16.55839.96277.852136.498219.978333.784474.200658.267887.1151169.1031483.2341889.9782318.3622859.9673417.0924120.1784826.5015698.0766572.0147640.5078694.3029981.26011237.41312748.50814225.455
824.807Fumitaka Yura
Tokyo, Japan
16.55839.96277.852136.498220.155334.200479.132663.436890.0971171.9991485.4771889.9782318.3622861.1683417.0924101.9094826.5015692.1286550.2677607.5078681.1869960.09011198.14112694.59614164.639
924.806Michail Svarichevsky
Gomel, Belarus
16.55839.96277.852136.498220.155334.200479.132663.926890.0971171.9991485.4771889.2752310.1752859.9673435.2064101.9094823.1065669.2346550.1617612.9248678.1569944.26711209.04112698.61814180.909
1024.776Frédéric van der Plancke
Brussels, Belgium
16.55839.96277.852136.498220.155334.200474.856663.436883.4111169.1031483.0421883.2842309.6342859.9673417.0924101.9094806.3675692.1286562.0187607.5078659.6899960.09011212.34312694.59614164.116
1124.717Ihar Korshunau
Gomel, Belarus
16.55839.96277.852136.498219.978333.784474.856657.762887.1151162.4541483.2341877.3782307.0372840.7733397.4024090.3354797.9365657.8066533.0987590.0948642.4109914.67811172.19012667.02814145.427
1224.644Yirmy Yasovsky
Rehovot, Israel
16.55839.96277.852136.498217.760329.740470.267651.972887.1151156.2371483.2341883.2842312.9222787.1493411.2504089.2074782.8845663.6186549.7817591.5218616.6339926.03511128.87712548.16314078.027
1324.540Michael Kolfman
Brooklyn, New York, United States
16.55839.96277.852136.498220.155334.200479.132662.260890.0971168.4251485.4771872.9832296.5102800.8203373.6004045.8644759.7975558.4346436.7637404.3218448.2119733.54310965.34812353.57513884.712
1424.508Alexander Alexandrov
St. Petersburg, Russia
16.55839.96277.852136.498218.157333.784472.111655.045883.4111150.4971464.7411846.0662292.0712812.2243387.8484044.9754783.8915546.9146524.8047402.0588632.2899685.19311169.07912367.58813844.537
1524.379Milan Delibasic
Belgrade, Serbia and Montenegro
16.55839.96277.852136.498220.155334.197478.610663.926883.4111153.8671473.6681846.9872279.8582789.8133350.2314005.6234715.9455521.0286366.7297354.5748396.7149579.89310818.55112212.27113664.419
1624.226Michael Rödel
Leipzig, Germany
16.55839.96277.852135.924218.157333.784470.267655.045875.3721149.4481460.5491839.2602240.4042758.9543290.9213944.8984651.5625458.2666341.8417284.8208409.1309618.03510862.27312197.89013752.304
1724.123Fred Mellender
Rochester, New York, United States
16.55839.96277.852136.498220.155334.197479.132663.926882.0431153.9881467.0551839.0002267.8122772.5563304.9593888.2284659.8355371.5126262.6087122.6528239.5889365.93110545.19712007.25513227.926
1824.065Jean-Marc Coutin
Boulogne-Billancourt, France
16.55839.96277.852136.498217.760333.784470.267652.070856.9481129.4851450.3231822.6972271.8312771.3633338.5143978.3984674.6135446.8666325.6477285.5828304.8399381.39310568.93511771.55713020.124
1923.668Nick Gardner
Portsmouth, England, United Kingdom
16.55839.96277.852136.498220.155334.197476.841663.284875.4331140.2151449.5851798.2812198.0962688.4563198.7603817.2844420.7955178.9815970.6166914.0447898.8489061.66510256.58911583.22713126.190
2023.643Michael Strauch
Ense, Germany
16.55839.96277.852134.020215.102311.769454.412652.174870.0681084.8661389.8411761.8012157.4402615.1783257.6323825.8524504.5055373.2476204.7517060.5438179.4559512.15110629.52711940.96213608.474
2123.309Marek Letowski
Krakow, Poland
16.55839.96277.852136.498220.155333.784469.468632.573832.9241091.3721386.2151715.6942135.1502607.4543138.4233743.7344404.1495131.6566052.7406751.6747933.3449058.54610204.36711485.01113086.623
2223.288Andreas Krimmer
Villingen, Baden-Würtemberg, Germany
16.55839.96277.852136.498220.155333.784478.610658.267867.5191136.3191401.9351797.9482189.0522737.1693072.4303973.3684499.4804617.2445982.2146862.2157987.5979236.5819853.51910152.28511162.324
2323.274Patryk Pomykalski
Gdynia, Poland
16.55839.96277.852136.498220.155334.200479.132662.260887.1151159.1361474.4461804.1192292.6412737.2383140.9733695.9684442.3554981.2835824.2046643.8517488.7418504.9379343.13610489.29011694.683
2423.261Borisas Bursteinas
London, England, United Kingdom
16.55839.96277.852136.498211.419321.534467.952626.184869.6101079.2701448.0801710.1842235.0352548.3213262.1473623.0754561.0834963.8406163.5126600.0098101.1038560.97710405.52210876.13713108.437
2523.020Ionel Santa
Bucharest, Romania
16.55839.96277.852136.498220.155334.200478.610661.896858.5391136.3941433.4671755.9632154.2482598.9433163.9043638.4354246.3284939.9655700.4566549.4357426.1758391.4319202.72411007.85212199.230
2621.929Kevin Burfitt
Melbourne, Victoria, Australia
16.55839.96277.852134.020212.312320.536443.736605.447827.4151041.3591321.8411645.4641999.0862420.5982886.5963421.9824019.7234683.2815416.1236274.0317160.4138126.4749175.67610311.48411495.665
2721.462Mark Mammel
Laurel, Maryland, United States
16.55839.96277.852130.184203.369306.526435.716592.403796.7971010.5241286.7511544.5371951.2532360.2362788.6793328.8623875.3014555.5605434.2526129.6347115.7697952.2419011.92910231.11311753.703
2821.094Tomek Czajka
Warsaw, Poland
16.55839.96277.852135.924215.064317.532435.731594.629781.773999.1961309.3351543.2601930.3132386.7272770.4063328.2764045.3404408.3614913.7565788.2196814.2637251.0798165.7489128.77910308.215
2920.896Gregor Heitkamp
Muenster, Germany
16.55839.96277.852134.098215.868296.934431.692588.901771.540972.7751232.2851545.3881880.0282315.2292783.1343140.5443899.9414653.4095121.6175829.4016593.6197284.2398281.1589377.85710337.500
3018.358Keith Schmidt
Piscataway, New Jersey, United States
16.55839.96277.852136.498216.819306.452416.209558.308710.352841.6991091.2001296.6811573.3261886.3892277.5262636.0373006.8543539.1283976.7724569.7794978.5715821.0146347.3397178.6578006.730
3117.984Simon Plantinga
Eelde, Netherlands
16.55839.96277.852133.650204.776291.143397.450526.829686.089871.1581084.3641343.8861603.4811891.4802212.0502562.3082987.9673512.3803940.6244447.0254928.8115416.3186032.1596693.9387673.953
3216.957Amrith Kumar
Framingham, Massachusetts, United States
16.55839.96277.852131.966195.526297.967396.218521.801651.155822.5031023.8071234.1511442.6911775.5371993.7972416.2982698.6053228.2703490.7684084.4624495.7344879.5135372.1805131.0296437.704
3316.025Hagen von Eitzen
Bonn, Germany
16.55839.96272.722127.840195.827302.622379.684526.792634.844824.3071005.7951146.2131416.3911624.3941973.2562069.3462286.8202769.6012966.9673373.3373765.8344233.4534561.3965309.4435707.539
3415.905Bernd Block
Ramsloh, Germany
16.55839.96277.852130.073190.820266.632365.170527.162612.521762.899960.4891143.1411306.0361572.2901799.1102207.7782498.1622693.4873129.0313609.7023855.7014305.9505046.5395241.9075747.506
3515.247Karl Grill
Vienna, Austria
16.55831.95854.45197.165137.819219.598284.733418.992515.086714.927848.4831126.9251304.4481674.4881902.4792377.1042662.0653254.2613602.6894325.4404743.8335610.1246104.9787127.7937705.603
3614.241Stephan Schwebel
Oxford, England, United Kingdom
16.55839.96277.755127.042178.366247.701364.023444.019570.343718.027856.391949.2891117.4151311.4441480.1101827.3541993.0342374.7622589.4072947.1583112.1923543.4803983.7543978.3694191.736
3714.070Alex Rand
Socorro, New Mexico, United States
16.55839.96277.852125.906173.989251.959356.290503.348646.613790.376999.1061299.4451395.8011710.9471743.9201995.8091951.5691919.4101636.4981943.9112373.1861991.7682189.2632237.3632295.373
3812.357Richard Kuhler
San Diego, California, United States
16.55839.96277.852136.498217.760318.301474.856635.225883.4111101.8781002.4981305.0751558.1751764.606           
3910.247George Eadon
Nashua, New Hampshire, United States
16.55839.96277.852136.498220.155328.227439.234577.352673.078714.606768.426790.916660.802            
409.706Eric Bainville
Genova, Italy
16.55839.96274.746131.968199.634276.340376.615487.972615.211787.123995.0241113.777             
417.503Thorsten Breuer
Wiesbaden, Germany
16.55839.96276.413104.033147.723182.665228.053269.335332.409414.087556.114581.417717.889            
427.139Venkatram Muddhasani
Bethlehem, Pennsylvania, United States
16.55839.96277.755130.748198.911234.920283.208387.811412.824                
436.907Peter Neugebauer
Göttingen, Germany
16.55839.96277.852135.924220.155333.784470.267                  
446.771Dzmitry Litskalau
Vitebsk, Belarus
16.55839.96277.852136.498220.155220.765316.845336.477                 
455.305Peter Mattsson
Edinburgh, Scotland, United Kingdom
16.55839.96277.755117.192120.856143.649147.580127.860                 
465.056Dumitru Ciubatii
Chisinau, Moldova
16.55837.08374.62689.144127.438169.867222.310                  
474.770Sattar Sattari
Tehran, Iran
16.55839.96277.755133.571174.516                    
484.609Andrés Olmos Sánchez
Bucaramanga, Colombia
16.55836.13959.35588.26198.750141.649217.354                  
494.442David Clark
Auckland, New Zealand
16.55839.96277.852134.020                    6590.076
504.237Sam Byrd
Little Rock, Arkansas, United States
16.55834.33257.40985.956121.727160.506                   
514.163Michael Shafer
East Lansing, Michigan, United States
16.55839.96273.33090.003123.738                    
523.883Adrian Sandor
Hong Kong, China
16.55839.96277.852120.522                     
533.260Carla Curtis
Hudson, New Hampshire, United States
16.55834.33258.12889.342                     
543.064Sarojkumar Sinha
Bishenpur, Manipur, India
15.45534.58451.29182.835                     
553.000Carlos Ungil
Geneva, Switzerland
16.55839.96277.852                      
562.000Steve Murray
Edgewood, Washington, United States
16.55839.962                       
562.000Shanming Loh
Singapore, Singapore
16.55839.962                       
581.904Georgios Papoutsis
Berlin, Germany
16.55836.139                       
591.859Seh Chun Ng
Klang, Selangor, Malaysia
16.55834.332                       
601.841John Metcalf
Lincolnshire, England, United Kingdom
16.55833.614                       
611.346Mark Sieklucki
Harwood Heights, Illinois, United States
16.55813.817                       
621.297Boris Alexeev
Athens, Georgia, United States
16.558     145.503                  
631.045Catalin Avram
Toronto, Ontario, Canada
11.58013.817                       
631.045Rajgopal Nayak
Mumbai, Maharashtra, India
11.58013.817                       
651.000Gunnar Andersson
Stockholm, Sweden
16.558                        
651.000J. B. Gill
Pleasant Grove, Utah, United States
16.558                        
651.000Bob Morrison
Wörth am Rhein, Germany
16.558                        
680.281David Greenspan
Cambridge, Massachusetts, United States
                        4033.422

Here are the best polyhedra submitted for each n:

N Area Faces Submitted By (earliest listed first)
4 16.558 (1,1,2),(2,3,4),(3,4,1);
(1,1,2),(2,3,4),(4,2,3);
(1,1,2),(3,4,1),(4,2,3);
(2,3,4),(3,4,1),(4,2,3).
Jim Gillogly, Georgios Papoutsis, John Metcalf, Ionel Santa, Borisas Bursteinas, Gunnar Andersson, Adrian Sandor, Jaroslaw Wroblewski, Pascal Zimmer, Frédéric van der Plancke, Ivan Kazmenko, Bob Morrison, Simon Plantinga, Peter Mattsson, Karl Grill, Seh Chun Ng, Michael Rödel, Peter Neugebauer, Carlos Ungil, Stephan Schwebel, Sam Byrd, Giorgio Di Falco, Alex Rand, Sattar Sattari, George Eadon, Marek Letowski, Steve Murray, Fred Mellender, Eric Bainville, Keith Schmidt, David Clark, Mark Mammel, Michail Svarichevsky, Nick Gardner, Richard Kuhler, Kevin Burfitt, Yirmy Yasovsky, Boris Alexeev, Michael Strauch, Amrith Kumar, Andreas Krimmer, Carla Curtis, Patryk Pomykalski, Michael Shafer, Gabriel Pîrvan, Fumitaka Yura, Venkatram Muddhasani, J. B. Gill, Jean-Marc Coutin, Andrés Olmos Sánchez, Hagen von Eitzen, Ihar Korshunau, Michael Kolfman, Gregor Heitkamp, Alexander Alexandrov, Bernd Block, Milan Delibasic, Dzmitry Litskalau, Thorsten Breuer, Tomek Czajka, Mark Beyleveld, Mark Sieklucki, Dumitru Ciubatii, Shanming Loh
5 39.962 (2,1,2),(1,4,5),(4,3,3);
(2,1,2),(1,4,5),(5,2,4);
(1,4,5),(3,5,1),(5,2,4);
(3,5,1),(2,1,2),(5,2,4);
(1,4,5),(3,5,1),(4,3,3);
(3,5,1),(2,1,2),(4,3,3).
Ionel Santa, Adrian Sandor, Jaroslaw Wroblewski, Pascal Zimmer, Simon Plantinga, Borisas Bursteinas, Michael Rödel, Jim Gillogly, Peter Neugebauer, Stephan Schwebel, Frédéric van der Plancke, Peter Mattsson, Giorgio Di Falco, Alex Rand, Ivan Kazmenko, George Eadon, Marek Letowski, Eric Bainville, Keith Schmidt, David Clark, Steve Murray, Carlos Ungil, Michail Svarichevsky, Fred Mellender, Richard Kuhler, Sattar Sattari, Kevin Burfitt, Michael Strauch, Mark Mammel, Amrith Kumar, Andreas Krimmer, Patryk Pomykalski, Gabriel Pîrvan, Fumitaka Yura, Yirmy Yasovsky, Nick Gardner, Hagen von Eitzen, Venkatram Muddhasani, Ihar Korshunau, Michael Shafer, Michael Kolfman, Gregor Heitkamp, Bernd Block, Mark Beyleveld, Alexander Alexandrov, Thorsten Breuer, Dzmitry Litskalau, Milan Delibasic, Jean-Marc Coutin, Tomek Czajka, Shanming Loh
6 77.852 (1,2,1),(2,4,6),(4,5,3);
(1,2,1),(2,4,6),(5,6,2);
(1,2,1),(3,3,5),(4,5,3);
(1,2,1),(3,3,5),(6,1,4);
(1,2,1),(5,6,2),(6,1,4);
(2,4,6),(4,5,3),(6,1,4);
(2,4,6),(5,6,2),(6,1,4);
(3,3,5),(4,5,3),(6,1,4).
Pascal Zimmer, Simon Plantinga, Borisas Bursteinas, Ionel Santa, Adrian Sandor, Jim Gillogly, Peter Neugebauer, Ivan Kazmenko, Alex Rand, Marek Letowski, Keith Schmidt, Giorgio Di Falco, Michael Rödel, Jaroslaw Wroblewski, George Eadon, Fred Mellender, Michael Strauch, Kevin Burfitt, Michail Svarichevsky, Richard Kuhler, David Clark, Amrith Kumar, Frédéric van der Plancke, Patryk Pomykalski, Carlos Ungil, Fumitaka Yura, Andreas Krimmer, Gabriel Pîrvan, Nick Gardner, Ihar Korshunau, Michael Kolfman, Bernd Block, Yirmy Yasovsky, Alexander Alexandrov, Milan Delibasic, Dzmitry Litskalau, Tomek Czajka, Gregor Heitkamp, Mark Beyleveld, Mark Mammel, Jean-Marc Coutin
7 136.498 (1,5,5),(6,7,1),(3,1,2);
(1,5,5),(6,7,1),(4,2,3);
(6,7,1),(7,4,7),(5,3,4);
(7,4,7),(1,5,5),(4,2,3);
(6,7,1),(7,4,7),(3,1,2);
(7,4,7),(1,5,5),(3,1,2);
(7,4,7),(4,2,3),(2,6,6);
(4,2,3),(6,7,1),(2,6,6);
(7,4,7),(2,6,6),(5,3,4);
(2,6,6),(6,7,1),(5,3,4).
Ionel Santa, Jim Gillogly, Pascal Zimmer, Ivan Kazmenko, Borisas Bursteinas, Jaroslaw Wroblewski, Michail Svarichevsky, Keith Schmidt, George Eadon, Marek Letowski, Giorgio Di Falco, Richard Kuhler, Fred Mellender, Patryk Pomykalski, Fumitaka Yura, Gabriel Pîrvan, Ihar Korshunau, Michael Kolfman, Frédéric van der Plancke, Andreas Krimmer, Nick Gardner, Mark Beyleveld, Alexander Alexandrov, Milan Delibasic, Dzmitry Litskalau, Yirmy Yasovsky, Jean-Marc Coutin
8 220.155 (2,1,5),(6,5,7),(1,8,2);
(2,1,5),(6,5,7),(8,4,1);
(5,7,6),(1,8,2),(8,4,1);
(3,2,3),(1,8,2),(8,4,1);
(3,2,3),(6,5,7),(1,8,2);
(3,2,3),(6,5,7),(8,4,1);
(7,6,8),(2,1,5),(1,8,2);
(7,6,8),(2,1,5),(8,4,1);
(4,3,4),(7,6,8),(1,8,2);
(4,3,4),(7,6,8),(8,4,1);
(5,7,6),(4,3,4),(1,8,2);
(5,7,6),(4,3,4),(8,4,1).
Jim Gillogly, Ivan Kazmenko, Peter Neugebauer, Pascal Zimmer, Fred Mellender, Ionel Santa, Michail Svarichevsky, Marek Letowski, Fumitaka Yura, George Eadon, Patryk Pomykalski, Gabriel Pîrvan, Michael Kolfman, Andreas Krimmer, Frédéric van der Plancke, Milan Delibasic, Nick Gardner, Mark Beyleveld, Dzmitry Litskalau
9 350.606 (1,9,5),(4,2,9),(7,6,3);
(1,9,5),(6,1,8),(7,6,3);
(1,9,5),(6,1,8),(9,5,2);
(3,8,4),(5,3,7),(8,4,1);
(1,9,5),(5,3,7),(8,4,1);
(3,8,4),(6,1,8),(9,5,2);
(3,8,4),(6,1,8),(8,4,1);
(1,9,5),(5,3,7),(9,5,2);
(3,8,4),(5,3,7),(9,5,2);
(1,9,5),(4,2,9),(8,4,1);
(2,7,6),(4,2,9),(8,4,1);
(2,7,6),(6,1,8),(8,4,1);
(2,7,6),(6,1,8),(7,6,3);
(2,7,6),(4,2,9),(7,6,3).
Pascal Zimmer
10 490.401 (1,10,5),(6,1,9),(8,6,3);
(1,10,5),(6,1,9),(10,5,2);
(3,9,4),(5,3,8),(9,4,1);
(1,10,5),(5,3,8),(9,4,1);
(3,9,4),(6,1,9),(10,5,2);
(3,9,4),(6,1,9),(9,4,1);
(1,10,5),(5,3,8),(10,5,2);
(3,9,4),(5,3,8),(10,5,2);
(1,10,5),(7,7,7),(8,6,3);
(1,10,5),(4,2,10),(9,4,1);
(2,8,6),(4,2,10),(9,4,1);
(2,8,6),(6,1,9),(9,4,1);
(2,8,6),(6,1,9),(8,6,3);
(1,10,5),(4,2,10),(7,7,7);
(2,8,6),(4,2,10),(8,6,3);
(4,2,10),(7,7,7),(8,6,3).
Pascal Zimmer
11 679.515 (3,10,5),(6,3,9),(10,6,1);
(1,11,6),(6,3,9),(10,6,1);
(3,10,5),(7,1,10),(10,6,1);
(3,10,5),(7,1,10),(9,8,2);
(1,11,6),(5,2,11),(11,7,3);
(2,9,7),(5,2,11),(11,7,3);
(2,9,7),(7,1,10),(10,6,1);
(2,9,7),(5,2,11),(10,6,1);
(1,11,6),(5,2,11),(8,5,4);
(1,11,6),(4,4,8),(8,5,4);
(1,11,6),(4,4,8),(10,6,1);
(4,4,8),(5,2,11),(8,5,4);
(4,4,8),(5,2,11),(10,6,1);
(3,10,5),(6,3,9),(9,8,2);
(1,11,6),(6,3,9),(9,8,2);
(1,11,6),(7,1,10),(9,8,2);
(1,11,6),(7,1,10),(11,7,3);
(2,9,7),(7,1,10),(11,7,3).
Pascal Zimmer
12 895.564 (1,12,6),(6,3,10),(12,5,1);
(2,10,7),(7,1,11),(12,5,1);
(3,11,5),(6,3,10),(12,5,1);
(3,11,5),(6,3,10),(11,7,2);
(3,11,5),(7,1,11),(12,5,1);
(3,11,5),(7,1,11),(11,7,2);
(1,12,6),(5,2,12),(12,5,1);
(2,10,7),(5,2,12),(12,5,1);
(1,12,6),(8,4,8),(9,8,3);
(1,12,6),(8,4,8),(10,9,4);
(1,12,6),(5,2,12),(10,9,4);
(2,10,7),(5,2,12),(10,9,4);
(1,12,6),(6,3,10),(11,7,2);
(1,12,6),(7,1,11),(11,7,2);
(1,12,6),(7,1,11),(9,8,3);
(2,10,7),(7,1,11),(9,8,3);
(2,10,7),(4,6,9),(9,8,3);
(4,6,9),(8,4,8),(9,8,3);
(2,10,7),(4,6,9),(8,4,8);
(2,10,7),(8,4,8),(10,9,4).
Pascal Zimmer
13 1193.317 (1,13,7),(7,3,11),(13,6,1);
(1,13,7),(7,3,11),(12,8,2);
(1,13,7),(8,1,12),(12,8,2);
(2,11,8),(6,2,13),(13,6,1);
(2,11,8),(8,1,12),(13,6,1);
(3,12,6),(7,3,11),(13,6,1);
(3,12,6),(7,3,11),(12,8,2);
(3,12,6),(8,1,12),(13,6,1);
(3,12,6),(8,1,12),(12,8,2);
(1,13,7),(8,1,12),(10,9,3);
(1,13,7),(6,2,13),(11,10,5);
(2,11,8),(8,1,12),(10,9,3);
(4,7,4),(6,2,13),(13,6,1);
(1,13,7),(5,5,10),(13,6,1);
(4,7,4),(5,5,10),(13,6,1);
(1,13,7),(9,4,9),(10,9,3);
(1,13,7),(9,4,9),(11,10,5);
(1,13,7),(4,7,4),(5,5,10);
(1,13,7),(4,7,4),(6,2,13);
(2,11,8),(9,4,9),(10,9,3);
(2,11,8),(6,2,13),(11,10,5);
(2,11,8),(9,4,9),(11,10,5).
Pascal Zimmer
14 1501.592 (1,14,8),(7,4,12),(13,6,1);
(1,14,8),(7,4,12),(14,7,3);
(1,14,8),(8,2,13),(14,7,3);
(3,13,7),(7,4,12),(13,6,1);
(3,13,7),(7,4,12),(14,7,3);
(3,13,7),(8,2,13),(13,6,1);
(3,13,7),(8,2,13),(14,7,3);
(1,14,8),(8,2,13),(12,10,2);
(2,12,9),(8,2,13),(13,6,1);
(2,12,9),(6,3,14),(13,6,1);
(4,1,10),(5,11,6),(11,5,4);
(1,14,8),(4,1,10),(13,6,1);
(4,1,10),(5,11,6),(13,6,1);
(5,11,6),(6,3,14),(11,5,4);
(5,11,6),(6,3,14),(13,6,1);
(2,12,9),(8,2,13),(12,10,2);
(1,14,8),(6,3,14),(10,9,5);
(1,14,8),(9,8,11),(10,9,5);
(1,14,8),(9,8,11),(12,10,2);
(2,12,9),(6,3,14),(12,10,2);
(1,14,8),(4,1,10),(11,5,4);
(1,14,8),(6,3,14),(11,5,4);
(6,3,14),(9,8,11),(10,9,5);
(6,3,14),(9,8,11),(12,10,2).
Pascal Zimmer
15 1889.978 (2,1,15),(11,10,10),(1,15,1);
(1,15,1),(2,1,15),(15,14,14);
(2,1,15),(15,14,14),(8,2,2);
(1,15,1),(15,14,14),(8,2,2);
(2,1,15),(8,2,2),(14,13,13);
(1,15,1),(8,2,2),(14,13,13);
(2,1,15),(14,13,13),(7,5,5);
(1,15,1),(14,13,13),(7,5,5);
(2,1,15),(7,5,5),(13,12,12);
(1,15,1),(7,5,5),(13,12,12);
(2,1,15),(13,12,12),(6,4,4);
(1,15,1),(13,12,12),(6,4,4);
(2,1,15),(6,4,4),(12,11,11);
(1,15,1),(6,4,4),(12,11,11);
(2,1,15),(12,11,11),(5,3,3);
(1,15,1),(12,11,11),(5,3,3);
(2,1,15),(5,3,3),(9,8,8);
(1,15,1),(5,3,3),(9,8,8);
(1,15,1),(4,6,6),(9,8,8);
(1,15,1),(4,6,6),(10,9,9);
(2,1,15),(9,8,8),(4,6,6);
(4,6,6),(2,1,15),(10,9,9);
(2,1,15),(10,9,9),(3,7,7);
(1,15,1),(10,9,9),(3,7,7);
(2,1,15),(3,7,7),(11,10,10);
(1,15,1),(3,7,7),(11,10,10).
Ivan Kazmenko, Jaroslaw Wroblewski, Jim Gillogly, Giorgio Di Falco, Mark Beyleveld, Fumitaka Yura
16 2318.362 (2,1,16),(16,2,2),(9,15,15);
(1,16,1),(16,2,2),(9,15,15);
(2,1,16),(9,15,15),(15,3,3);
(1,16,1),(9,15,15),(15,3,3);
(2,1,16),(15,3,3),(8,14,14);
(1,16,1),(15,3,3),(8,14,14);
(2,1,16),(8,14,14),(14,4,4);
(1,16,1),(8,14,14),(14,4,4);
(2,1,16),(14,4,4),(7,12,12);
(1,16,1),(14,4,4),(7,12,12);
(2,1,16),(7,12,12),(13,5,5);
(1,16,1),(7,12,12),(13,5,5);
(2,1,16),(13,5,5),(6,13,13);
(1,16,1),(13,5,5),(6,13,13);
(2,1,16),(6,13,13),(12,6,6);
(1,16,1),(6,13,13),(12,6,6);
(2,1,16),(12,6,6),(3,9,9);
(1,16,1),(12,6,6),(3,9,9);
(2,1,16),(3,9,9),(11,7,7);
(1,16,1),(3,9,9),(11,7,7);
(2,1,16),(11,7,7),(4,10,10);
(1,16,1),(11,7,7),(4,10,10);
(2,1,16),(4,10,10),(10,8,8);
(1,16,1),(4,10,10),(10,8,8);
(2,1,16),(1,16,1),(16,2,2);
(1,16,1),(10,8,8),(5,11,11);
(5,11,11),(1,16,1),(2,1,16);
(2,1,16),(5,11,11),(10,8,8).
Ivan Kazmenko, Jaroslaw Wroblewski, Pascal Zimmer, Jim Gillogly, Gabriel Pîrvan, Fumitaka Yura, Giorgio Di Falco
17 2861.168 (2,9,16),(15,16,3),(17,1,17);
(2,9,16),(16,17,2),(17,1,17);
(3,8,15),(14,15,4),(17,1,17);
(3,8,15),(15,16,3),(17,1,17);
(5,7,13),(14,15,4),(17,1,17);
(1,2,1),(2,9,16),(15,16,3);
(1,2,1),(2,9,16),(16,17,2);
(1,2,1),(3,8,15),(14,15,4);
(1,2,1),(3,8,15),(15,16,3);
(4,6,14),(13,14,5),(17,1,17);
(5,7,13),(13,14,5),(17,1,17);
(1,2,1),(5,7,13),(14,15,4);
(1,2,1),(4,6,14),(13,14,5);
(1,2,1),(5,7,13),(13,14,5);
(1,2,1),(16,17,2),(17,1,17);
(4,6,14),(10,11,8),(17,1,17);
(1,2,1),(4,6,14),(10,11,8);
(7,5,11),(10,11,8),(17,1,17);
(6,3,12),(9,10,9),(17,1,17);
(7,5,11),(9,10,9),(17,1,17);
(1,2,1),(6,3,12),(9,10,9);
(1,2,1),(7,5,11),(9,10,9);
(1,2,1),(7,5,11),(10,11,8);
(1,2,1),(6,3,12),(11,12,7);
(1,2,1),(8,4,10),(11,12,7);
(1,2,1),(12,13,6),(17,1,17);
(1,2,1),(8,4,10),(12,13,6);
(8,4,10),(12,13,6),(17,1,17);
(6,3,12),(11,12,7),(17,1,17);
(8,4,10),(11,12,7),(17,1,17).
Pascal Zimmer, Ivan Kazmenko, Fumitaka Yura, Giorgio Di Falco
18 3437.491 (1,1,1),(2,10,17),(15,17,3);
(1,1,1),(2,10,17),(16,18,2);
(1,1,1),(3,9,16),(14,16,4);
(1,1,1),(3,9,16),(15,17,3);
(1,1,1),(13,15,5),(17,5,15);
(1,1,1),(14,16,4),(17,5,15);
(1,1,1),(16,18,2),(18,2,18);
(2,10,17),(15,17,3),(18,2,18);
(2,10,17),(16,18,2),(18,2,18);
(3,9,16),(14,16,4),(18,2,18);
(3,9,16),(15,17,3),(18,2,18);
(5,8,13),(13,15,5),(17,5,15);
(5,8,13),(13,15,5),(18,2,18);
(5,8,13),(14,16,4),(17,5,15);
(5,8,13),(14,16,4),(18,2,18);
(1,1,1),(4,7,14),(13,15,5);
(1,1,1),(12,14,6),(18,2,18);
(4,7,14),(13,15,5),(18,2,18);
(8,3,10),(11,13,7),(18,2,18);
(8,3,10),(12,14,6),(18,2,18);
(1,1,1),(8,3,10),(12,14,6);
(6,4,12),(11,13,7),(18,2,18);
(1,1,1),(4,7,14),(10,12,8);
(1,1,1),(7,6,11),(10,12,8);
(1,1,1),(6,4,12),(9,11,9);
(1,1,1),(7,6,11),(9,11,9);
(6,4,12),(9,11,9),(18,2,18);
(4,7,14),(10,12,8),(18,2,18);
(1,1,1),(6,4,12),(11,13,7);
(1,1,1),(8,3,10),(11,13,7);
(7,6,11),(9,11,9),(18,2,18);
(7,6,11),(10,12,8),(18,2,18).
Pascal Zimmer
19 4120.178 (1,18,2),(10,2,18),(18,1,1);
(1,18,2),(10,2,18),(19,19,19);
(1,18,2),(18,1,1),(19,19,19);
(2,17,3),(10,2,18),(18,1,1);
(2,17,3),(10,2,18),(19,19,19);
(2,17,3),(11,3,17),(18,1,1);
(2,17,3),(11,3,17),(19,19,19);
(3,16,4),(11,3,17),(18,1,1);
(3,16,4),(11,3,17),(19,19,19);
(3,16,4),(12,6,14),(18,1,1);
(3,16,4),(12,6,14),(19,19,19);
(4,15,5),(12,6,14),(18,1,1);
(4,15,5),(12,6,14),(19,19,19);
(4,15,5),(13,5,15),(18,1,1);
(4,15,5),(13,5,15),(19,19,19);
(5,14,6),(13,5,15),(18,1,1);
(5,14,6),(13,5,15),(19,19,19);
(5,14,6),(14,4,16),(18,1,1);
(5,14,6),(14,4,16),(19,19,19);
(6,13,7),(17,9,11),(18,1,1);
(6,13,7),(17,9,11),(19,19,19);
(6,13,7),(18,1,1),(19,19,19);
(7,12,8),(16,8,12),(18,1,1);
(7,12,8),(16,8,12),(19,19,19);
(7,12,8),(17,9,11),(18,1,1);
(7,12,8),(17,9,11),(19,19,19);
(8,11,9),(15,7,13),(18,1,1);
(8,11,9),(15,7,13),(19,19,19);
(8,11,9),(16,8,12),(18,1,1);
(8,11,9),(16,8,12),(19,19,19);
(9,10,10),(14,4,16),(18,1,1);
(9,10,10),(14,4,16),(19,19,19);
(9,10,10),(15,7,13),(18,1,1);
(9,10,10),(15,7,13),(19,19,19).
Jaroslaw Wroblewski, Ivan Kazmenko, Giorgio Di Falco, Mark Beyleveld
20 4830.553 (4,19,18),(1,2,1),(19,10,3);
(4,19,18),(20,1,20),(19,10,3);
(17,11,5),(4,19,18),(1,2,1);
(5,18,17),(17,11,5),(1,2,1);
(18,8,2),(5,18,17),(1,2,1);
(18,8,2),(5,18,17),(20,1,20);
(6,17,16),(18,8,2),(1,2,1);
(6,17,16),(18,8,2),(20,1,20);
(16,9,4),(6,17,16),(1,2,1);
(16,9,4),(6,17,16),(20,1,20);
(11,12,11),(16,9,4),(1,2,1);
(11,12,11),(16,9,4),(20,1,20);
(15,6,7),(11,12,11),(1,2,1);
(15,6,7),(11,12,11),(20,1,20);
(10,13,12),(15,6,7),(1,2,1);
(10,13,12),(15,6,7),(20,1,20);
(14,5,8),(10,13,12),(1,2,1);
(14,5,8),(10,13,12),(20,1,20);
(9,14,13),(14,5,8),(1,2,1);
(9,14,13),(14,5,8),(20,1,20);
(13,4,9),(9,14,13),(1,2,1);
(13,4,9),(9,14,13),(20,1,20);
(13,4,9),(8,15,14),(1,2,1);
(13,4,9),(8,15,14),(20,1,20);
(8,15,14),(12,3,10),(1,2,1);
(8,15,14),(12,3,10),(20,1,20);
(3,20,19),(1,2,1),(20,1,20);
(3,20,19),(1,2,1),(19,10,3);
(3,20,19),(20,1,20),(19,10,3);
(7,16,15),(12,3,10),(1,2,1);
(7,16,15),(12,3,10),(20,1,20);
(7,16,15),(1,2,1),(20,1,20);
(2,7,6),(5,18,17),(17,11,5);
(2,7,6),(5,18,17),(20,1,20);
(2,7,6),(4,19,18),(17,11,5);
(2,7,6),(4,19,18),(20,1,20).
Giorgio Di Falco
21 5698.076 (1,20,2),(11,2,20),(20,1,1);
(1,20,2),(11,2,20),(21,21,21);
(1,20,2),(20,1,1),(21,21,21);
(2,19,3),(11,2,20),(20,1,1);
(2,19,3),(11,2,20),(21,21,21);
(2,19,3),(12,3,19),(20,1,1);
(2,19,3),(12,3,19),(21,21,21);
(3,18,4),(12,3,19),(20,1,1);
(3,18,4),(12,3,19),(21,21,21);
(3,18,4),(13,7,15),(20,1,1);
(3,18,4),(13,7,15),(21,21,21);
(4,17,5),(13,7,15),(20,1,1);
(4,17,5),(13,7,15),(21,21,21);
(4,17,5),(14,6,16),(20,1,1);
(4,17,5),(14,6,16),(21,21,21);
(5,16,6),(14,6,16),(20,1,1);
(5,16,6),(14,6,16),(21,21,21);
(5,16,6),(15,5,17),(20,1,1);
(5,16,6),(15,5,17),(21,21,21);
(6,15,7),(15,5,17),(20,1,1);
(6,15,7),(15,5,17),(21,21,21);
(6,15,7),(16,4,18),(20,1,1);
(6,15,7),(16,4,18),(21,21,21);
(7,14,8),(19,10,12),(20,1,1);
(7,14,8),(19,10,12),(21,21,21);
(7,14,8),(20,1,1),(21,21,21);
(8,13,9),(18,9,13),(20,1,1);
(8,13,9),(18,9,13),(21,21,21);
(8,13,9),(19,10,12),(20,1,1);
(8,13,9),(19,10,12),(21,21,21);
(9,12,10),(17,8,14),(20,1,1);
(9,12,10),(17,8,14),(21,21,21);
(9,12,10),(18,9,13),(20,1,1);
(9,12,10),(18,9,13),(21,21,21);
(10,11,11),(16,4,18),(20,1,1);
(10,11,11),(16,4,18),(21,21,21);
(10,11,11),(17,8,14),(20,1,1);
(10,11,11),(17,8,14),(21,21,21).
Jaroslaw Wroblewski, Ivan Kazmenko, Mark Beyleveld
22 6615.399 (4,11,20),(6,7,2),(19,20,5);
(4,11,20),(6,7,2),(20,21,4);
(1,2,1),(2,12,21),(20,21,4);
(1,2,1),(4,11,20),(20,21,4);
(1,2,1),(4,11,20),(19,20,5);
(1,2,1),(5,10,18),(19,20,5);
(1,2,1),(5,10,18),(18,19,6);
(1,2,1),(3,8,19),(18,19,6);
(1,2,1),(3,8,19),(17,18,7);
(1,2,1),(7,9,17),(17,18,7);
(1,2,1),(7,9,17),(12,13,12);
(1,2,1),(8,6,16),(12,13,12);
(1,2,1),(8,6,16),(13,14,11);
(1,2,1),(9,5,15),(13,14,11);
(1,2,1),(9,5,15),(14,15,10);
(1,2,1),(10,4,14),(14,15,10);
(1,2,1),(10,4,14),(15,16,9);
(1,2,1),(11,3,13),(15,16,9);
(1,2,1),(11,3,13),(16,17,8);
(1,2,1),(16,17,8),(22,1,22);
(1,2,1),(21,22,3),(22,1,22);
(1,2,1),(2,12,21),(21,22,3);
(2,12,21),(20,21,4),(22,1,22);
(6,7,2),(20,21,4),(22,1,22);
(6,7,2),(19,20,5),(22,1,22);
(5,10,18),(19,20,5),(22,1,22);
(5,10,18),(18,19,6),(22,1,22);
(3,8,19),(18,19,6),(22,1,22);
(3,8,19),(17,18,7),(22,1,22);
(7,9,17),(17,18,7),(22,1,22);
(7,9,17),(12,13,12),(22,1,22);
(8,6,16),(12,13,12),(22,1,22);
(8,6,16),(13,14,11),(22,1,22);
(9,5,15),(13,14,11),(22,1,22);
(9,5,15),(14,15,10),(22,1,22);
(10,4,14),(14,15,10),(22,1,22);
(10,4,14),(15,16,9),(22,1,22);
(11,3,13),(15,16,9),(22,1,22);
(11,3,13),(16,17,8),(22,1,22);
(2,12,21),(21,22,3),(22,1,22).
Pascal Zimmer
23 7642.872 (1,1,23),(23,2,2),(12,22,22);
(2,23,1),(23,2,2),(12,22,22);
(1,1,23),(12,22,22),(22,3,3);
(2,23,1),(12,22,22),(22,3,3);
(1,1,23),(22,3,3),(11,21,21);
(2,23,1),(22,3,3),(11,21,21);
(1,1,23),(11,21,21),(21,4,4);
(2,23,1),(11,21,21),(21,4,4);
(1,1,23),(21,4,4),(10,20,20);
(2,23,1),(21,4,4),(10,20,20);
(1,1,23),(10,20,20),(20,5,5);
(2,23,1),(10,20,20),(20,5,5);
(1,1,23),(20,5,5),(9,17,17);
(2,23,1),(20,5,5),(9,17,17);
(1,1,23),(9,17,17),(19,6,6);
(2,23,1),(9,17,17),(19,6,6);
(1,1,23),(19,6,6),(8,18,18);
(2,23,1),(19,6,6),(8,18,18);
(1,1,23),(8,18,18),(18,7,7);
(2,23,1),(8,18,18),(18,7,7);
(1,1,23),(18,7,7),(7,19,19);
(2,23,1),(18,7,7),(7,19,19);
(1,1,23),(7,19,19),(14,11,11);
(2,23,1),(7,19,19),(14,11,11);
(1,1,23),(14,11,11),(6,15,15);
(2,23,1),(14,11,11),(6,15,15);
(1,1,23),(6,15,15),(13,12,12);
(2,23,1),(6,15,15),(13,12,12);
(1,1,23),(13,12,12),(4,16,16);
(2,23,1),(13,12,12),(4,16,16);
(1,1,23),(4,16,16),(15,10,10);
(2,23,1),(4,16,16),(15,10,10);
(1,1,23),(15,10,10),(5,14,14);
(2,23,1),(15,10,10),(5,14,14);
(1,1,23),(5,14,14),(16,9,9);
(2,23,1),(5,14,14),(16,9,9);
(1,1,23),(16,9,9),(3,13,13);
(2,23,1),(16,9,9),(3,13,13);
(1,1,23),(3,13,13),(17,8,8);
(2,23,1),(3,13,13),(17,8,8);
(23,2,2),(1,1,23),(2,23,1);
(17,8,8),(1,1,23),(2,23,1).
Ivan Kazmenko, Giorgio Di Falco
24 8759.328 (1,1,1),(3,13,23),(21,23,3);
(1,1,1),(3,13,23),(22,24,2);
(1,1,1),(4,12,22),(20,22,4);
(1,1,1),(4,12,22),(21,23,3);
(1,1,1),(5,8,19),(13,15,11);
(1,1,1),(5,8,19),(17,19,7);
(1,1,1),(7,10,17),(17,19,7);
(1,1,1),(7,10,17),(18,20,6);
(1,1,1),(6,11,18),(18,20,6);
(1,1,1),(6,11,18),(19,21,5);
(1,1,1),(9,7,15),(13,15,11);
(1,1,1),(9,7,15),(12,14,12);
(1,1,1),(8,5,16),(12,14,12);
(1,1,1),(8,5,16),(14,16,10);
(1,1,1),(10,4,14),(14,16,10);
(1,1,1),(10,4,14),(15,17,9);
(1,1,1),(11,3,13),(15,17,9);
(1,1,1),(11,3,13),(16,18,8);
(1,1,1),(16,18,8),(24,2,24);
(1,1,1),(19,21,5),(23,6,20);
(1,1,1),(20,22,4),(23,6,20);
(1,1,1),(22,24,2),(24,2,24);
(3,13,23),(21,23,3),(24,2,24);
(3,13,23),(22,24,2),(24,2,24);
(4,12,22),(20,22,4),(24,2,24);
(4,12,22),(21,23,3),(24,2,24);
(2,9,21),(19,21,5),(23,6,20);
(2,9,21),(19,21,5),(24,2,24);
(2,9,21),(20,22,4),(23,6,20);
(2,9,21),(20,22,4),(24,2,24);
(5,8,19),(13,15,11),(24,2,24);
(5,8,19),(17,19,7),(24,2,24);
(7,10,17),(17,19,7),(24,2,24);
(7,10,17),(18,20,6),(24,2,24);
(6,11,18),(18,20,6),(24,2,24);
(6,11,18),(19,21,5),(24,2,24);
(9,7,15),(13,15,11),(24,2,24);
(9,7,15),(12,14,12),(24,2,24);
(8,5,16),(12,14,12),(24,2,24);
(8,5,16),(14,16,10),(24,2,24);
(10,4,14),(14,16,10),(24,2,24);
(10,4,14),(15,17,9),(24,2,24);
(11,3,13),(15,17,9),(24,2,24);
(11,3,13),(16,18,8),(24,2,24).
Pascal Zimmer
25 9981.260 (1,24,2),(13,2,24),(24,1,1);
(1,24,2),(13,2,24),(25,25,25);
(1,24,2),(24,1,1),(25,25,25);
(2,23,3),(13,2,24),(24,1,1);
(2,23,3),(13,2,24),(25,25,25);
(2,23,3),(14,3,23),(24,1,1);
(2,23,3),(14,3,23),(25,25,25);
(3,22,4),(14,3,23),(24,1,1);
(3,22,4),(14,3,23),(25,25,25);
(3,22,4),(15,4,22),(24,1,1);
(3,22,4),(15,4,22),(25,25,25);
(4,21,5),(15,4,22),(24,1,1);
(4,21,5),(15,4,22),(25,25,25);
(4,21,5),(16,8,18),(24,1,1);
(4,21,5),(16,8,18),(25,25,25);
(5,20,6),(16,8,18),(24,1,1);
(5,20,6),(16,8,18),(25,25,25);
(5,20,6),(17,7,19),(24,1,1);
(5,20,6),(17,7,19),(25,25,25);
(6,19,7),(17,7,19),(24,1,1);
(6,19,7),(17,7,19),(25,25,25);
(6,19,7),(18,6,20),(24,1,1);
(6,19,7),(18,6,20),(25,25,25);
(7,18,8),(18,6,20),(24,1,1);
(7,18,8),(18,6,20),(25,25,25);
(7,18,8),(19,5,21),(24,1,1);
(7,18,8),(19,5,21),(25,25,25);
(8,17,9),(23,12,14),(24,1,1);
(8,17,9),(23,12,14),(25,25,25);
(8,17,9),(24,1,1),(25,25,25);
(9,16,10),(22,11,15),(24,1,1);
(9,16,10),(22,11,15),(25,25,25);
(9,16,10),(23,12,14),(24,1,1);
(9,16,10),(23,12,14),(25,25,25);
(10,15,11),(21,10,16),(24,1,1);
(10,15,11),(21,10,16),(25,25,25);
(10,15,11),(22,11,15),(24,1,1);
(10,15,11),(22,11,15),(25,25,25);
(11,14,12),(20,9,17),(24,1,1);
(11,14,12),(20,9,17),(25,25,25);
(11,14,12),(21,10,16),(24,1,1);
(11,14,12),(21,10,16),(25,25,25);
(12,13,13),(19,5,21),(24,1,1);
(12,13,13),(19,5,21),(25,25,25);
(12,13,13),(20,9,17),(24,1,1);
(12,13,13),(20,9,17),(25,25,25).
Jaroslaw Wroblewski, Ivan Kazmenko, Pascal Zimmer, Mark Beyleveld
26 11317.942 (1,1,1),(2,14,25),(23,25,3);
(1,1,1),(2,14,25),(24,26,2);
(1,1,1),(3,13,24),(22,24,4);
(1,1,1),(3,13,24),(23,25,3);
(1,1,1),(4,11,23),(21,23,5);
(1,1,1),(4,11,23),(22,24,4);
(1,1,1),(5,8,21),(13,15,13);
(1,1,1),(5,8,21),(18,20,8);
(1,1,1),(6,9,20),(18,20,8);
(1,1,1),(6,9,20),(19,21,7);
(1,1,1),(7,10,19),(19,21,7);
(1,1,1),(7,10,19),(20,22,6);
(1,1,1),(9,7,18),(13,15,13);
(1,1,1),(9,7,18),(14,16,12);
(1,1,1),(10,5,16),(14,16,12);
(1,1,1),(10,5,16),(15,17,11);
(1,1,1),(11,4,15),(15,17,11);
(1,1,1),(11,4,15),(16,18,10);
(1,1,1),(12,3,14),(16,18,10);
(1,1,1),(12,3,14),(17,19,9);
(1,1,1),(17,19,9),(26,2,26);
(1,1,1),(20,22,6),(25,6,22);
(1,1,1),(21,23,5),(25,6,22);
(1,1,1),(24,26,2),(26,2,26);
(2,14,25),(23,25,3),(26,2,26);
(2,14,25),(24,26,2),(26,2,26);
(3,13,24),(22,24,4),(26,2,26);
(3,13,24),(23,25,3),(26,2,26);
(4,11,23),(21,23,5),(26,2,26);
(4,11,23),(22,24,4),(26,2,26);
(5,8,21),(13,15,13),(26,2,26);
(5,8,21),(18,20,8),(26,2,26);
(6,9,20),(18,20,8),(26,2,26);
(6,9,20),(19,21,7),(26,2,26);
(7,10,19),(19,21,7),(26,2,26);
(7,10,19),(20,22,6),(26,2,26);
(8,12,17),(20,22,6),(25,6,22);
(8,12,17),(20,22,6),(26,2,26);
(8,12,17),(21,23,5),(25,6,22);
(8,12,17),(21,23,5),(26,2,26);
(9,7,18),(13,15,13),(26,2,26);
(9,7,18),(14,16,12),(26,2,26);
(10,5,16),(14,16,12),(26,2,26);
(10,5,16),(15,17,11),(26,2,26);
(11,4,15),(15,17,11),(26,2,26);
(11,4,15),(16,18,10),(26,2,26);
(12,3,14),(16,18,10),(26,2,26);
(12,3,14),(17,19,9),(26,2,26).
Pascal Zimmer
27 12748.508 (1,26,2),(14,2,26),(26,1,1);
(1,26,2),(14,2,26),(27,27,27);
(1,26,2),(26,1,1),(27,27,27);
(2,25,3),(14,2,26),(26,1,1);
(2,25,3),(14,2,26),(27,27,27);
(2,25,3),(15,3,25),(26,1,1);
(2,25,3),(15,3,25),(27,27,27);
(3,24,4),(15,3,25),(26,1,1);
(3,24,4),(15,3,25),(27,27,27);
(3,24,4),(16,4,24),(26,1,1);
(3,24,4),(16,4,24),(27,27,27);
(4,23,5),(16,4,24),(26,1,1);
(4,23,5),(16,4,24),(27,27,27);
(4,23,5),(17,9,19),(26,1,1);
(4,23,5),(17,9,19),(27,27,27);
(5,22,6),(17,9,19),(26,1,1);
(5,22,6),(17,9,19),(27,27,27);
(5,22,6),(18,8,20),(26,1,1);
(5,22,6),(18,8,20),(27,27,27);
(6,21,7),(18,8,20),(26,1,1);
(6,21,7),(18,8,20),(27,27,27);
(6,21,7),(19,7,21),(26,1,1);
(6,21,7),(19,7,21),(27,27,27);
(7,20,8),(19,7,21),(26,1,1);
(7,20,8),(19,7,21),(27,27,27);
(7,20,8),(20,6,22),(26,1,1);
(7,20,8),(20,6,22),(27,27,27);
(8,19,9),(20,6,22),(26,1,1);
(8,19,9),(20,6,22),(27,27,27);
(8,19,9),(21,5,23),(26,1,1);
(8,19,9),(21,5,23),(27,27,27);
(9,18,10),(25,13,15),(26,1,1);
(9,18,10),(25,13,15),(27,27,27);
(9,18,10),(26,1,1),(27,27,27);
(10,17,11),(24,12,16),(26,1,1);
(10,17,11),(24,12,16),(27,27,27);
(10,17,11),(25,13,15),(26,1,1);
(10,17,11),(25,13,15),(27,27,27);
(11,16,12),(23,11,17),(26,1,1);
(11,16,12),(23,11,17),(27,27,27);
(11,16,12),(24,12,16),(26,1,1);
(11,16,12),(24,12,16),(27,27,27);
(12,15,13),(22,10,18),(26,1,1);
(12,15,13),(22,10,18),(27,27,27);
(12,15,13),(23,11,17),(26,1,1);
(12,15,13),(23,11,17),(27,27,27);
(13,14,14),(21,5,23),(26,1,1);
(13,14,14),(21,5,23),(27,27,27);
(13,14,14),(22,10,18),(26,1,1);
(13,14,14),(22,10,18),(27,27,27).
Jaroslaw Wroblewski, Pascal Zimmer, Ivan Kazmenko
28 14334.688 (1,1,1),(2,15,27),(25,27,3);
(1,1,1),(2,15,27),(26,28,2);
(1,1,1),(3,14,26),(24,26,4);
(1,1,1),(3,14,26),(25,27,3);
(1,1,1),(4,12,25),(23,25,5);
(1,1,1),(4,12,25),(24,26,4);
(1,1,1),(5,8,23),(14,16,14);
(1,1,1),(5,8,23),(19,21,9);
(1,1,1),(6,9,22),(19,21,9);
(1,1,1),(6,9,22),(20,22,8);
(1,1,1),(7,10,21),(20,22,8);
(1,1,1),(7,10,21),(21,23,7);
(1,1,1),(8,11,20),(21,23,7);
(1,1,1),(8,11,20),(22,24,6);
(1,1,1),(10,7,19),(14,16,14);
(1,1,1),(10,7,19),(15,17,13);
(1,1,1),(11,5,17),(15,17,13);
(1,1,1),(11,5,17),(16,18,12);
(1,1,1),(12,4,16),(16,18,12);
(1,1,1),(12,4,16),(17,19,11);
(1,1,1),(13,3,15),(17,19,11);
(1,1,1),(13,3,15),(18,20,10);
(1,1,1),(18,20,10),(28,2,28);
(1,1,1),(22,24,6),(27,6,24);
(1,1,1),(23,25,5),(27,6,24);
(1,1,1),(26,28,2),(28,2,28);
(2,15,27),(25,27,3),(28,2,28);
(2,15,27),(26,28,2),(28,2,28);
(3,14,26),(24,26,4),(28,2,28);
(3,14,26),(25,27,3),(28,2,28);
(4,12,25),(23,25,5),(28,2,28);
(4,12,25),(24,26,4),(28,2,28);
(5,8,23),(14,16,14),(28,2,28);
(5,8,23),(19,21,9),(28,2,28);
(6,9,22),(19,21,9),(28,2,28);
(6,9,22),(20,22,8),(28,2,28);
(7,10,21),(20,22,8),(28,2,28);
(7,10,21),(21,23,7),(28,2,28);
(8,11,20),(21,23,7),(28,2,28);
(8,11,20),(22,24,6),(28,2,28);
(9,13,18),(22,24,6),(27,6,24);
(9,13,18),(22,24,6),(28,2,28);
(9,13,18),(23,25,5),(27,6,24);
(9,13,18),(23,25,5),(28,2,28);
(10,7,19),(14,16,14),(28,2,28);
(10,7,19),(15,17,13),(28,2,28);
(11,5,17),(15,17,13),(28,2,28);
(11,5,17),(16,18,12),(28,2,28);
(12,4,16),(16,18,12),(28,2,28);
(12,4,16),(17,19,11),(28,2,28);
(13,3,15),(17,19,11),(28,2,28);
(13,3,15),(18,20,10),(28,2,28).
Pascal Zimmer

Here is the history of each n, showing when and by whom each new record was achieved:

NDate and TimeNew AreaRecord Set By
43/21 10:54 AM11.580Adrian Sandor
3/22 04:48 PM16.558Jim Gillogly
53/21 10:54 AM13.817Adrian Sandor
3/22 05:42 PM36.139Georgios Papoutsis
3/23 10:44 AM39.962Ionel Santa
63/23 10:44 AM72.810Ionel Santa
3/24 07:25 AM77.755Jaroslaw Wroblewski
3/24 12:17 PM77.852Pascal Zimmer
73/23 10:44 AM108.894Ionel Santa
3/24 07:25 AM131.484Jaroslaw Wroblewski
3/30 10:40 AM135.924Borisas Bursteinas
3/30 10:48 AM136.498Ionel Santa
83/23 10:44 AM172.019Ionel Santa
3/24 07:25 AM209.516Jaroslaw Wroblewski
3/30 10:48 AM212.050Ionel Santa
3/30 10:55 PM218.157Ionel Santa
4/01 09:08 PM220.155Jim Gillogly
93/23 10:44 AM255.665Ionel Santa
3/24 07:25 AM312.558Jaroslaw Wroblewski
3/30 10:48 AM313.249Ionel Santa
3/30 10:55 PM328.990Ionel Santa
3/31 07:07 PM333.784Ionel Santa
4/07 07:09 PM334.197Pascal Zimmer
4/17 09:01 PM334.200Ionel Santa
6/22 11:00 AM350.606Pascal Zimmer
103/23 10:44 AM318.282Ionel Santa
3/24 07:25 AM438.752Jaroslaw Wroblewski
3/27 08:31 AM442.440Jaroslaw Wroblewski
3/30 10:55 PM470.267Ionel Santa
4/02 11:32 PM474.200Ivan Kazmenko
4/05 04:40 PM474.856Ivan Kazmenko
4/07 07:09 PM479.132Pascal Zimmer
6/22 11:00 AM490.401Pascal Zimmer
113/23 10:44 AM399.934Ionel Santa
3/24 01:46 AM413.660Ivan Kazmenko
3/24 07:25 AM598.375Jaroslaw Wroblewski
3/27 08:31 AM602.366Jaroslaw Wroblewski
3/31 07:46 AM638.304Jaroslaw Wroblewski
4/01 01:18 AM656.394Ivan Kazmenko
4/02 11:32 PM659.339Ivan Kazmenko
4/07 07:09 PM662.260Pascal Zimmer
4/12 11:23 AM663.926Michail Svarichevsky
6/22 11:00 AM679.515Pascal Zimmer
123/23 10:44 AM545.232Ionel Santa
3/24 07:25 AM794.781Jaroslaw Wroblewski
3/27 08:31 AM797.086Jaroslaw Wroblewski
3/31 07:46 AM850.627Jaroslaw Wroblewski
4/01 01:18 AM878.822Ivan Kazmenko
4/05 11:06 AM881.288Jaroslaw Wroblewski
4/07 07:09 PM890.097Pascal Zimmer
6/22 11:00 AM895.564Pascal Zimmer
133/23 10:44 AM651.563Ionel Santa
3/24 07:25 AM1,039.397Jaroslaw Wroblewski
3/27 08:31 AM1,040.763Jaroslaw Wroblewski
3/31 07:46 AM1,096.857Jaroslaw Wroblewski
4/01 01:18 AM1,157.754Ivan Kazmenko
4/08 09:30 AM1,159.770Michail Svarichevsky
4/08 06:04 PM1,163.021Pascal Zimmer
4/09 07:39 AM1,169.103Jaroslaw Wroblewski
4/09 02:37 PM1,171.999Pascal Zimmer
6/22 11:00 AM1,193.317Pascal Zimmer
143/23 10:44 AM807.144Ionel Santa
3/24 07:25 AM1,315.492Jaroslaw Wroblewski
3/27 08:31 AM1,319.002Jaroslaw Wroblewski
3/30 10:55 PM1,391.201Ionel Santa
3/31 07:46 AM1,411.281Jaroslaw Wroblewski
4/01 01:18 AM1,462.699Ivan Kazmenko
4/02 11:32 PM1,465.082Ivan Kazmenko
4/06 11:13 PM1,466.386Ivan Kazmenko
4/08 09:30 AM1,472.997Michail Svarichevsky
4/08 06:04 PM1,485.477Pascal Zimmer
5/29 10:56 AM1,489.843Gabriel Pîrvan
6/13 05:55 PM1,501.592Pascal Zimmer
153/23 10:44 AM1,001.315Ionel Santa
3/24 07:25 AM1,634.428Jaroslaw Wroblewski
3/27 08:31 AM1,644.633Jaroslaw Wroblewski
3/31 07:46 AM1,765.450Jaroslaw Wroblewski
4/01 01:18 AM1,855.543Ivan Kazmenko
4/02 11:32 PM1,864.236Ivan Kazmenko
4/09 07:39 AM1,883.284Jaroslaw Wroblewski
4/10 02:17 AM1,889.978Ivan Kazmenko
163/23 10:44 AM1,167.362Ionel Santa
3/24 07:25 AM2,008.523Jaroslaw Wroblewski
3/27 08:31 AM2,012.838Jaroslaw Wroblewski
3/31 07:46 AM2,176.290Jaroslaw Wroblewski
4/01 01:18 AM2,286.917Ivan Kazmenko
4/05 10:35 PM2,290.564Ivan Kazmenko
4/08 09:30 AM2,294.859Michail Svarichevsky
4/09 07:39 AM2,309.634Jaroslaw Wroblewski
4/10 02:17 AM2,318.362Ivan Kazmenko
173/23 10:44 AM1,389.919Ionel Santa
3/24 07:25 AM2,432.733Jaroslaw Wroblewski
3/31 07:46 AM2,654.777Jaroslaw Wroblewski
4/01 01:18 AM2,752.777Ivan Kazmenko
4/05 12:38 PM2,758.954Michael Rödel
4/05 10:35 PM2,805.293Ivan Kazmenko
4/06 11:13 PM2,829.075Ivan Kazmenko
4/09 07:39 AM2,859.967Jaroslaw Wroblewski
5/05 05:18 PM2,861.168Pascal Zimmer
183/23 10:44 AM1,561.968Ionel Santa
3/24 07:25 AM2,910.104Jaroslaw Wroblewski
3/27 08:31 AM2,921.503Jaroslaw Wroblewski
3/31 07:46 AM3,186.825Jaroslaw Wroblewski
4/01 01:18 AM3,301.417Ivan Kazmenko
4/02 11:32 PM3,319.422Ivan Kazmenko
4/06 11:13 PM3,398.272Ivan Kazmenko
4/09 07:39 AM3,401.614Jaroslaw Wroblewski
4/10 09:05 PM3,405.238Michail Svarichevsky
4/11 06:45 PM3,415.030Ivan Kazmenko
4/12 10:36 AM3,417.092Jaroslaw Wroblewski
5/02 07:15 PM3,435.206Pascal Zimmer
5/05 05:18 PM3,437.491Pascal Zimmer
193/23 10:44 AM1,917.150Ionel Santa
3/24 07:25 AM3,459.890Jaroslaw Wroblewski
3/27 08:31 AM3,460.264Jaroslaw Wroblewski
3/31 07:46 AM3,771.279Jaroslaw Wroblewski
4/01 01:18 AM3,876.586Ivan Kazmenko
4/02 11:32 PM3,920.638Ivan Kazmenko
4/05 12:38 PM3,944.898Michael Rödel
4/05 04:40 PM3,951.278Ivan Kazmenko
4/06 11:13 PM4,032.624Ivan Kazmenko
4/08 09:30 AM4,040.425Michail Svarichevsky
4/08 05:39 PM4,066.584Michail Svarichevsky
4/09 07:39 AM4,101.909Jaroslaw Wroblewski
4/10 09:06 AM4,120.178Jaroslaw Wroblewski
203/23 10:44 AM2,185.016Ionel Santa
3/24 07:25 AM4,062.772Jaroslaw Wroblewski
3/31 07:46 AM4,473.108Jaroslaw Wroblewski
4/01 01:18 AM4,585.066Ivan Kazmenko
4/02 11:32 PM4,630.821Ivan Kazmenko
4/05 12:38 PM4,651.562Michael Rödel
4/06 11:13 PM4,785.909Ivan Kazmenko
4/09 07:39 AM4,806.367Jaroslaw Wroblewski
4/10 02:17 AM4,816.641Ivan Kazmenko
4/12 10:36 AM4,826.501Jaroslaw Wroblewski
5/05 05:18 PM4,828.843Pascal Zimmer
6/06 07:20 PM4,830.174Pascal Zimmer
6/22 01:06 AM4,830.553Giorgio Di Falco
213/23 10:44 AM2,444.076Ionel Santa
3/24 07:25 AM4,728.451Jaroslaw Wroblewski
3/27 08:31 AM4,730.592Jaroslaw Wroblewski
3/31 07:46 AM5,203.803Jaroslaw Wroblewski
4/01 01:18 AM5,387.502Ivan Kazmenko
4/05 12:38 PM5,458.266Michael Rödel
4/05 04:40 PM5,527.483Ivan Kazmenko
4/06 11:13 PM5,656.676Ivan Kazmenko
4/09 07:39 AM5,692.128Jaroslaw Wroblewski
4/10 09:06 AM5,698.076Jaroslaw Wroblewski
223/23 10:44 AM2,698.578Ionel Santa
3/24 07:25 AM5,441.573Jaroslaw Wroblewski
3/27 08:31 AM5,468.178Jaroslaw Wroblewski
3/31 07:46 AM6,013.519Jaroslaw Wroblewski
4/01 01:18 AM6,174.026Ivan Kazmenko
4/02 11:32 PM6,207.382Ivan Kazmenko
4/05 12:38 PM6,341.841Michael Rödel
4/05 04:40 PM6,364.725Ivan Kazmenko
4/05 10:35 PM6,497.333Ivan Kazmenko
4/06 11:13 PM6,525.541Ivan Kazmenko
4/08 05:39 PM6,537.413Michail Svarichevsky
4/09 07:39 AM6,537.951Jaroslaw Wroblewski
4/11 04:08 AM6,550.267Ivan Kazmenko
4/11 06:45 PM6,557.459Ivan Kazmenko
4/12 10:36 AM6,572.014Jaroslaw Wroblewski
4/29 05:01 PM6,585.450Pascal Zimmer
6/02 04:59 PM6,613.925Jim Gillogly
6/06 07:20 PM6,615.399Pascal Zimmer
233/23 10:44 AM3,128.144Ionel Santa
3/24 07:25 AM6,284.369Jaroslaw Wroblewski
3/31 07:46 AM6,930.259Jaroslaw Wroblewski
4/01 01:18 AM7,062.684Ivan Kazmenko
4/02 11:32 PM7,275.291Ivan Kazmenko
4/05 12:38 PM7,284.820Michael Rödel
4/05 10:35 PM7,458.689Ivan Kazmenko
4/06 11:13 PM7,577.915Ivan Kazmenko
4/09 07:39 AM7,607.507Jaroslaw Wroblewski
4/10 09:06 AM7,640.507Jaroslaw Wroblewski
5/21 11:13 PM7,642.872Ivan Kazmenko
243/23 10:44 AM3,519.784Ionel Santa
3/24 07:25 AM7,152.638Jaroslaw Wroblewski
3/27 08:31 AM7,171.031Jaroslaw Wroblewski
3/31 07:46 AM7,891.086Jaroslaw Wroblewski
4/01 01:18 AM8,019.295Ivan Kazmenko
4/02 11:32 PM8,273.527Ivan Kazmenko
4/05 12:38 PM8,409.130Michael Rödel
4/05 10:35 PM8,526.467Ivan Kazmenko
4/06 12:21 AM8,545.399Ivan Kazmenko
4/06 11:13 PM8,610.246Ivan Kazmenko
4/08 05:39 PM8,670.413Michail Svarichevsky
4/11 04:08 AM8,679.229Ivan Kazmenko
4/12 10:36 AM8,694.302Jaroslaw Wroblewski
4/29 05:01 PM8,737.750Pascal Zimmer
6/05 05:47 PM8,759.328Pascal Zimmer
253/23 10:44 AM3,714.873Ionel Santa
3/24 07:25 AM8,106.887Jaroslaw Wroblewski
3/27 08:31 AM8,148.751Jaroslaw Wroblewski
3/31 07:46 AM8,983.149Jaroslaw Wroblewski
4/01 01:18 AM9,247.092Ivan Kazmenko
4/05 02:23 AM9,249.279Michael Rödel
4/05 12:38 PM9,618.035Michael Rödel
4/06 12:21 AM9,664.570Ivan Kazmenko
4/06 11:13 PM9,862.961Ivan Kazmenko
4/08 05:39 PM9,873.324Michail Svarichevsky
4/09 07:39 AM9,960.090Jaroslaw Wroblewski
4/10 09:06 AM9,981.260Jaroslaw Wroblewski
263/23 10:44 AM4,257.773Ionel Santa
3/24 07:25 AM9,170.861Jaroslaw Wroblewski
3/27 08:31 AM9,199.265Jaroslaw Wroblewski
3/31 07:46 AM10,153.071Jaroslaw Wroblewski
4/01 01:18 AM10,364.224Ivan Kazmenko
4/02 11:32 PM10,613.141Ivan Kazmenko
4/05 12:38 PM10,862.273Michael Rödel
4/05 10:35 PM10,935.905Ivan Kazmenko
4/06 11:13 PM11,105.123Ivan Kazmenko
4/08 05:39 PM11,167.072Michail Svarichevsky
4/09 12:41 AM11,203.548Ivan Kazmenko
4/11 06:45 PM11,221.173Ivan Kazmenko
4/12 10:36 AM11,237.413Jaroslaw Wroblewski
4/29 05:01 PM11,317.942Pascal Zimmer
273/23 10:44 AM4,826.997Ionel Santa
3/24 07:25 AM10,306.159Jaroslaw Wroblewski
3/27 08:31 AM10,341.306Jaroslaw Wroblewski
3/31 07:46 AM11,352.117Jaroslaw Wroblewski
4/01 01:18 AM11,924.302Ivan Kazmenko
4/02 11:32 PM11,963.444Ivan Kazmenko
4/05 12:38 PM12,197.890Michael Rödel
4/05 10:35 PM12,312.364Ivan Kazmenko
4/06 11:13 PM12,649.568Ivan Kazmenko
4/09 07:39 AM12,694.596Jaroslaw Wroblewski
4/10 09:06 AM12,748.508Jaroslaw Wroblewski
283/23 10:44 AM5,281.477Ionel Santa
3/24 07:25 AM11,528.870Jaroslaw Wroblewski
3/27 08:31 AM11,567.534Jaroslaw Wroblewski
3/31 07:46 AM12,752.999Jaroslaw Wroblewski
4/01 01:18 AM13,558.499Ivan Kazmenko
4/02 11:32 PM13,579.096Ivan Kazmenko
4/05 12:38 PM13,752.304Michael Rödel
4/05 04:40 PM13,817.000Ivan Kazmenko
4/06 11:13 PM14,093.078Ivan Kazmenko
4/09 12:41 AM14,202.239Ivan Kazmenko
4/12 10:36 AM14,225.455Jaroslaw Wroblewski
4/29 05:01 PM14,334.688Pascal Zimmer

My thanks to everyone who participated.

Al Zimmermann
Lausanne, Switzerland
June 23, 2003


Al Zimmermann’s Programming ContestsPolyhedra Contest Description

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