Polytope of Type {2,10,8,3} with group SmallGroup(1920,240195)

s0 := (1,2);;
s1 := ( 11, 35)( 12, 36)( 13, 37)( 14, 38)( 15, 39)( 16, 40)( 17, 41)( 18, 42)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 25, 33)( 26, 34)( 51, 75)( 52, 76)( 53, 77)( 54, 78)( 55, 79)( 56, 80)( 57, 81)( 58, 82)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)( 64, 72)( 65, 73)( 66, 74)( 91,115)( 92,116)( 93,117)( 94,118)( 95,119)( 96,120)( 97,121)( 98,122)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)(105,113)(106,114)(131,155)(132,156)(133,157)(134,158)(135,159)(136,160)(137,161)(138,162)(139,147)(140,148)(141,149)(142,150)(143,151)(144,152)(145,153)(146,154)(171,195)(172,196)(173,197)(174,198)(175,199)(176,200)(177,201)(178,202)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)(185,193)(186,194)(211,235)(212,236)(213,237)(214,238)(215,239)(216,240)(217,241)(218,242)(219,227)(220,228)(221,229)(222,230)(223,231)(224,232)(225,233)(226,234);;
s2 := (  3,135)(  4,136)(  5,138)(  6,137)(  7,132)(  8,131)(  9,133)( 10,134)( 11,127)( 12,128)( 13,130)( 14,129)( 15,124)( 16,123)( 17,125)( 18,126)( 19,159)( 20,160)( 21,162)( 22,161)( 23,156)( 24,155)( 25,157)( 26,158)( 27,151)( 28,152)( 29,154)( 30,153)( 31,148)( 32,147)( 33,149)( 34,150)( 35,143)( 36,144)( 37,146)( 38,145)( 39,140)( 40,139)( 41,141)( 42,142)( 43,175)( 44,176)( 45,178)( 46,177)( 47,172)( 48,171)( 49,173)( 50,174)( 51,167)( 52,168)( 53,170)( 54,169)( 55,164)( 56,163)( 57,165)( 58,166)( 59,199)( 60,200)( 61,202)( 62,201)( 63,196)( 64,195)( 65,197)( 66,198)( 67,191)( 68,192)( 69,194)( 70,193)( 71,188)( 72,187)( 73,189)( 74,190)( 75,183)( 76,184)( 77,186)( 78,185)( 79,180)( 80,179)( 81,181)( 82,182)( 83,215)( 84,216)( 85,218)( 86,217)( 87,212)( 88,211)( 89,213)( 90,214)( 91,207)( 92,208)( 93,210)( 94,209)( 95,204)( 96,203)( 97,205)( 98,206)( 99,239)(100,240)(101,242)(102,241)(103,236)(104,235)(105,237)(106,238)(107,231)(108,232)(109,234)(110,233)(111,228)(112,227)(113,229)(114,230)(115,223)(116,224)(117,226)(118,225)(119,220)(120,219)(121,221)(122,222);;
s3 := (  5,  8)(  6,  7)(  9, 10)( 13, 16)( 14, 15)( 17, 18)( 21, 24)( 22, 23)( 25, 26)( 29, 32)( 30, 31)( 33, 34)( 37, 40)( 38, 39)( 41, 42)( 43, 83)( 44, 84)( 45, 88)( 46, 87)( 47, 86)( 48, 85)( 49, 90)( 50, 89)( 51, 91)( 52, 92)( 53, 96)( 54, 95)( 55, 94)( 56, 93)( 57, 98)( 58, 97)( 59, 99)( 60,100)( 61,104)( 62,103)( 63,102)( 64,101)( 65,106)( 66,105)( 67,107)( 68,108)( 69,112)( 70,111)( 71,110)( 72,109)( 73,114)( 74,113)( 75,115)( 76,116)( 77,120)( 78,119)( 79,118)( 80,117)( 81,122)( 82,121)(123,124)(125,127)(126,128)(131,132)(133,135)(134,136)(139,140)(141,143)(142,144)(147,148)(149,151)(150,152)(155,156)(157,159)(158,160)(163,204)(164,203)(165,207)(166,208)(167,205)(168,206)(169,209)(170,210)(171,212)(172,211)(173,215)(174,216)(175,213)(176,214)(177,217)(178,218)(179,220)(180,219)(181,223)(182,224)(183,221)(184,222)(185,225)(186,226)(187,228)(188,227)(189,231)(190,232)(191,229)(192,230)(193,233)(194,234)(195,236)(196,235)(197,239)(198,240)(199,237)(200,238)(201,241)(202,242);;
s4 := (  3, 83)(  4, 84)(  5, 89)(  6, 90)(  7, 88)(  8, 87)(  9, 85)( 10, 86)( 11, 91)( 12, 92)( 13, 97)( 14, 98)( 15, 96)( 16, 95)( 17, 93)( 18, 94)( 19, 99)( 20,100)( 21,105)( 22,106)( 23,104)( 24,103)( 25,101)( 26,102)( 27,107)( 28,108)( 29,113)( 30,114)( 31,112)( 32,111)( 33,109)( 34,110)( 35,115)( 36,116)( 37,121)( 38,122)( 39,120)( 40,119)( 41,117)( 42,118)( 45, 49)( 46, 50)( 47, 48)( 53, 57)( 54, 58)( 55, 56)( 61, 65)( 62, 66)( 63, 64)( 69, 73)( 70, 74)( 71, 72)( 77, 81)( 78, 82)( 79, 80)(123,204)(124,203)(125,210)(126,209)(127,207)(128,208)(129,206)(130,205)(131,212)(132,211)(133,218)(134,217)(135,215)(136,216)(137,214)(138,213)(139,220)(140,219)(141,226)(142,225)(143,223)(144,224)(145,222)(146,221)(147,228)(148,227)(149,234)(150,233)(151,231)(152,232)(153,230)(154,229)(155,236)(156,235)(157,242)(158,241)(159,239)(160,240)(161,238)(162,237)(163,164)(165,170)(166,169)(171,172)(173,178)(174,177)(179,180)(181,186)(182,185)(187,188)(189,194)(190,193)(195,196)(197,202)(198,201);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s4*s3*s2*s4*s3*s2*s3*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(242)!(1,2);
s1 := Sym(242)!( 11, 35)( 12, 36)( 13, 37)( 14, 38)( 15, 39)( 16, 40)( 17, 41)( 18, 42)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 25, 33)( 26, 34)( 51, 75)( 52, 76)( 53, 77)( 54, 78)( 55, 79)( 56, 80)( 57, 81)( 58, 82)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)( 64, 72)( 65, 73)( 66, 74)( 91,115)( 92,116)( 93,117)( 94,118)( 95,119)( 96,120)( 97,121)( 98,122)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)(105,113)(106,114)(131,155)(132,156)(133,157)(134,158)(135,159)(136,160)(137,161)(138,162)(139,147)(140,148)(141,149)(142,150)(143,151)(144,152)(145,153)(146,154)(171,195)(172,196)(173,197)(174,198)(175,199)(176,200)(177,201)(178,202)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)(185,193)(186,194)(211,235)(212,236)(213,237)(214,238)(215,239)(216,240)(217,241)(218,242)(219,227)(220,228)(221,229)(222,230)(223,231)(224,232)(225,233)(226,234);
s2 := Sym(242)!(  3,135)(  4,136)(  5,138)(  6,137)(  7,132)(  8,131)(  9,133)( 10,134)( 11,127)( 12,128)( 13,130)( 14,129)( 15,124)( 16,123)( 17,125)( 18,126)( 19,159)( 20,160)( 21,162)( 22,161)( 23,156)( 24,155)( 25,157)( 26,158)( 27,151)( 28,152)( 29,154)( 30,153)( 31,148)( 32,147)( 33,149)( 34,150)( 35,143)( 36,144)( 37,146)( 38,145)( 39,140)( 40,139)( 41,141)( 42,142)( 43,175)( 44,176)( 45,178)( 46,177)( 47,172)( 48,171)( 49,173)( 50,174)( 51,167)( 52,168)( 53,170)( 54,169)( 55,164)( 56,163)( 57,165)( 58,166)( 59,199)( 60,200)( 61,202)( 62,201)( 63,196)( 64,195)( 65,197)( 66,198)( 67,191)( 68,192)( 69,194)( 70,193)( 71,188)( 72,187)( 73,189)( 74,190)( 75,183)( 76,184)( 77,186)( 78,185)( 79,180)( 80,179)( 81,181)( 82,182)( 83,215)( 84,216)( 85,218)( 86,217)( 87,212)( 88,211)( 89,213)( 90,214)( 91,207)( 92,208)( 93,210)( 94,209)( 95,204)( 96,203)( 97,205)( 98,206)( 99,239)(100,240)(101,242)(102,241)(103,236)(104,235)(105,237)(106,238)(107,231)(108,232)(109,234)(110,233)(111,228)(112,227)(113,229)(114,230)(115,223)(116,224)(117,226)(118,225)(119,220)(120,219)(121,221)(122,222);
s3 := Sym(242)!(  5,  8)(  6,  7)(  9, 10)( 13, 16)( 14, 15)( 17, 18)( 21, 24)( 22, 23)( 25, 26)( 29, 32)( 30, 31)( 33, 34)( 37, 40)( 38, 39)( 41, 42)( 43, 83)( 44, 84)( 45, 88)( 46, 87)( 47, 86)( 48, 85)( 49, 90)( 50, 89)( 51, 91)( 52, 92)( 53, 96)( 54, 95)( 55, 94)( 56, 93)( 57, 98)( 58, 97)( 59, 99)( 60,100)( 61,104)( 62,103)( 63,102)( 64,101)( 65,106)( 66,105)( 67,107)( 68,108)( 69,112)( 70,111)( 71,110)( 72,109)( 73,114)( 74,113)( 75,115)( 76,116)( 77,120)( 78,119)( 79,118)( 80,117)( 81,122)( 82,121)(123,124)(125,127)(126,128)(131,132)(133,135)(134,136)(139,140)(141,143)(142,144)(147,148)(149,151)(150,152)(155,156)(157,159)(158,160)(163,204)(164,203)(165,207)(166,208)(167,205)(168,206)(169,209)(170,210)(171,212)(172,211)(173,215)(174,216)(175,213)(176,214)(177,217)(178,218)(179,220)(180,219)(181,223)(182,224)(183,221)(184,222)(185,225)(186,226)(187,228)(188,227)(189,231)(190,232)(191,229)(192,230)(193,233)(194,234)(195,236)(196,235)(197,239)(198,240)(199,237)(200,238)(201,241)(202,242);
s4 := Sym(242)!(  3, 83)(  4, 84)(  5, 89)(  6, 90)(  7, 88)(  8, 87)(  9, 85)( 10, 86)( 11, 91)( 12, 92)( 13, 97)( 14, 98)( 15, 96)( 16, 95)( 17, 93)( 18, 94)( 19, 99)( 20,100)( 21,105)( 22,106)( 23,104)( 24,103)( 25,101)( 26,102)( 27,107)( 28,108)( 29,113)( 30,114)( 31,112)( 32,111)( 33,109)( 34,110)( 35,115)( 36,116)( 37,121)( 38,122)( 39,120)( 40,119)( 41,117)( 42,118)( 45, 49)( 46, 50)( 47, 48)( 53, 57)( 54, 58)( 55, 56)( 61, 65)( 62, 66)( 63, 64)( 69, 73)( 70, 74)( 71, 72)( 77, 81)( 78, 82)( 79, 80)(123,204)(124,203)(125,210)(126,209)(127,207)(128,208)(129,206)(130,205)(131,212)(132,211)(133,218)(134,217)(135,215)(136,216)(137,214)(138,213)(139,220)(140,219)(141,226)(142,225)(143,223)(144,224)(145,222)(146,221)(147,228)(148,227)(149,234)(150,233)(151,231)(152,232)(153,230)(154,229)(155,236)(156,235)(157,242)(158,241)(159,239)(160,240)(161,238)(162,237)(163,164)(165,170)(166,169)(171,172)(173,178)(174,177)(179,180)(181,186)(182,185)(187,188)(189,194)(190,193)(195,196)(197,202)(198,201);
poly := sub<Sym(242)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s4*s3*s2*s4*s3*s2*s3*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

Overview

Special Properties

Related Polytopes

Quotients maximal quotients in bold

Covers minimal covers in bold

Representations