Polytope of Type {2,118,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,118,4}*1888
if this polytope has a name.
Group : SmallGroup(1888,182)
Rank : 4
Schlafli Type : {2,118,4}
Number of vertices, edges, etc : 2, 118, 236, 4
Order of s₀s₁s₂s₃ : 236
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,118,2}*944
   4-fold quotients : {2,59,2}*472
   59-fold quotients : {2,2,4}*32
   118-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

to this polytope