Polytope of Type {2,4,6,10} with group SmallGroup(1920,240407)

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

Permutation Representation (Magma)

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

Overview

Special Properties

Related Polytopes

Quotients maximal quotients in bold

Covers minimal covers in bold

Representations