Polytope of Type {4,90}

s0 := ( 91,136)( 92,137)( 93,138)( 94,139)( 95,140)( 96,141)( 97,142)( 98,143)( 99,144)(100,145)(101,146)(102,147)(103,148)(104,149)(105,150)(106,151)(107,152)(108,153)(109,154)(110,155)(111,156)(112,157)(113,158)(114,159)(115,160)(116,161)(117,162)(118,163)(119,164)(120,165)(121,166)(122,167)(123,168)(124,169)(125,170)(126,171)(127,172)(128,173)(129,174)(130,175)(131,176)(132,177)(133,178)(134,179)(135,180);;
s1 := (  1, 91)(  2, 93)(  3, 92)(  4,103)(  5,105)(  6,104)(  7,100)(  8,102)(  9,101)( 10, 97)( 11, 99)( 12, 98)( 13, 94)( 14, 96)( 15, 95)( 16,123)( 17,122)( 18,121)( 19,135)( 20,134)( 21,133)( 22,132)( 23,131)( 24,130)( 25,129)( 26,128)( 27,127)( 28,126)( 29,125)( 30,124)( 31,108)( 32,107)( 33,106)( 34,120)( 35,119)( 36,118)( 37,117)( 38,116)( 39,115)( 40,114)( 41,113)( 42,112)( 43,111)( 44,110)( 45,109)( 46,136)( 47,138)( 48,137)( 49,148)( 50,150)( 51,149)( 52,145)( 53,147)( 54,146)( 55,142)( 56,144)( 57,143)( 58,139)( 59,141)( 60,140)( 61,168)( 62,167)( 63,166)( 64,180)( 65,179)( 66,178)( 67,177)( 68,176)( 69,175)( 70,174)( 71,173)( 72,172)( 73,171)( 74,170)( 75,169)( 76,153)( 77,152)( 78,151)( 79,165)( 80,164)( 81,163)( 82,162)( 83,161)( 84,160)( 85,159)( 86,158)( 87,157)( 88,156)( 89,155)( 90,154);;
s2 := (  1, 19)(  2, 21)(  3, 20)(  4, 16)(  5, 18)(  6, 17)(  7, 28)(  8, 30)(  9, 29)( 10, 25)( 11, 27)( 12, 26)( 13, 22)( 14, 24)( 15, 23)( 31, 36)( 32, 35)( 33, 34)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 46, 64)( 47, 66)( 48, 65)( 49, 61)( 50, 63)( 51, 62)( 52, 73)( 53, 75)( 54, 74)( 55, 70)( 56, 72)( 57, 71)( 58, 67)( 59, 69)( 60, 68)( 76, 81)( 77, 80)( 78, 79)( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 91,109)( 92,111)( 93,110)( 94,106)( 95,108)( 96,107)( 97,118)( 98,120)( 99,119)(100,115)(101,117)(102,116)(103,112)(104,114)(105,113)(121,126)(122,125)(123,124)(127,135)(128,134)(129,133)(130,132)(136,154)(137,156)(138,155)(139,151)(140,153)(141,152)(142,163)(143,165)(144,164)(145,160)(146,162)(147,161)(148,157)(149,159)(150,158)(166,171)(167,170)(168,169)(172,180)(173,179)(174,178)(175,177);;
poly := Group([s0,s1,s2]);;

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

s0 := Sym(180)!( 91,136)( 92,137)( 93,138)( 94,139)( 95,140)( 96,141)( 97,142)( 98,143)( 99,144)(100,145)(101,146)(102,147)(103,148)(104,149)(105,150)(106,151)(107,152)(108,153)(109,154)(110,155)(111,156)(112,157)(113,158)(114,159)(115,160)(116,161)(117,162)(118,163)(119,164)(120,165)(121,166)(122,167)(123,168)(124,169)(125,170)(126,171)(127,172)(128,173)(129,174)(130,175)(131,176)(132,177)(133,178)(134,179)(135,180);
s1 := Sym(180)!(  1, 91)(  2, 93)(  3, 92)(  4,103)(  5,105)(  6,104)(  7,100)(  8,102)(  9,101)( 10, 97)( 11, 99)( 12, 98)( 13, 94)( 14, 96)( 15, 95)( 16,123)( 17,122)( 18,121)( 19,135)( 20,134)( 21,133)( 22,132)( 23,131)( 24,130)( 25,129)( 26,128)( 27,127)( 28,126)( 29,125)( 30,124)( 31,108)( 32,107)( 33,106)( 34,120)( 35,119)( 36,118)( 37,117)( 38,116)( 39,115)( 40,114)( 41,113)( 42,112)( 43,111)( 44,110)( 45,109)( 46,136)( 47,138)( 48,137)( 49,148)( 50,150)( 51,149)( 52,145)( 53,147)( 54,146)( 55,142)( 56,144)( 57,143)( 58,139)( 59,141)( 60,140)( 61,168)( 62,167)( 63,166)( 64,180)( 65,179)( 66,178)( 67,177)( 68,176)( 69,175)( 70,174)( 71,173)( 72,172)( 73,171)( 74,170)( 75,169)( 76,153)( 77,152)( 78,151)( 79,165)( 80,164)( 81,163)( 82,162)( 83,161)( 84,160)( 85,159)( 86,158)( 87,157)( 88,156)( 89,155)( 90,154);
s2 := Sym(180)!(  1, 19)(  2, 21)(  3, 20)(  4, 16)(  5, 18)(  6, 17)(  7, 28)(  8, 30)(  9, 29)( 10, 25)( 11, 27)( 12, 26)( 13, 22)( 14, 24)( 15, 23)( 31, 36)( 32, 35)( 33, 34)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 46, 64)( 47, 66)( 48, 65)( 49, 61)( 50, 63)( 51, 62)( 52, 73)( 53, 75)( 54, 74)( 55, 70)( 56, 72)( 57, 71)( 58, 67)( 59, 69)( 60, 68)( 76, 81)( 77, 80)( 78, 79)( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 91,109)( 92,111)( 93,110)( 94,106)( 95,108)( 96,107)( 97,118)( 98,120)( 99,119)(100,115)(101,117)(102,116)(103,112)(104,114)(105,113)(121,126)(122,125)(123,124)(127,135)(128,134)(129,133)(130,132)(136,154)(137,156)(138,155)(139,151)(140,153)(141,152)(142,163)(143,165)(144,164)(145,160)(146,162)(147,161)(148,157)(149,159)(150,158)(166,171)(167,170)(168,169)(172,180)(173,179)(174,178)(175,177);
poly := sub<Sym(180)|s0,s1,s2>;

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