Polytope of Type {122,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {122,4}*976
Also Known As : {122,4|2}. if this polytope has another name.
Group : SmallGroup(976,39)
Rank : 3
Schlafli Type : {122,4}
Number of vertices, edges, etc : 122, 244, 4
Order of s₀s₁s₂ : 244
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {122,4,2} of size 1952
Vertex Figure Of :
   {2,122,4} of size 1952
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {122,2}*488
   4-fold quotients : {61,2}*244
   61-fold quotients : {2,4}*16
   122-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {244,4}*1952, {122,8}*1952
Permutation Representation (GAP) :

s0 := (  2, 61)(  3, 60)(  4, 59)(  5, 58)(  6, 57)(  7, 56)(  8, 55)(  9, 54)
( 10, 53)( 11, 52)( 12, 51)( 13, 50)( 14, 49)( 15, 48)( 16, 47)( 17, 46)
( 18, 45)( 19, 44)( 20, 43)( 21, 42)( 22, 41)( 23, 40)( 24, 39)( 25, 38)
( 26, 37)( 27, 36)( 28, 35)( 29, 34)( 30, 33)( 31, 32)( 63,122)( 64,121)
( 65,120)( 66,119)( 67,118)( 68,117)( 69,116)( 70,115)( 71,114)( 72,113)
( 73,112)( 74,111)( 75,110)( 76,109)( 77,108)( 78,107)( 79,106)( 80,105)
( 81,104)( 82,103)( 83,102)( 84,101)( 85,100)( 86, 99)( 87, 98)( 88, 97)
( 89, 96)( 90, 95)( 91, 94)( 92, 93)(124,183)(125,182)(126,181)(127,180)
(128,179)(129,178)(130,177)(131,176)(132,175)(133,174)(134,173)(135,172)
(136,171)(137,170)(138,169)(139,168)(140,167)(141,166)(142,165)(143,164)
(144,163)(145,162)(146,161)(147,160)(148,159)(149,158)(150,157)(151,156)
(152,155)(153,154)(185,244)(186,243)(187,242)(188,241)(189,240)(190,239)
(191,238)(192,237)(193,236)(194,235)(195,234)(196,233)(197,232)(198,231)
(199,230)(200,229)(201,228)(202,227)(203,226)(204,225)(205,224)(206,223)
(207,222)(208,221)(209,220)(210,219)(211,218)(212,217)(213,216)(214,215);;
s1 := (  1,  2)(  3, 61)(  4, 60)(  5, 59)(  6, 58)(  7, 57)(  8, 56)(  9, 55)
( 10, 54)( 11, 53)( 12, 52)( 13, 51)( 14, 50)( 15, 49)( 16, 48)( 17, 47)
( 18, 46)( 19, 45)( 20, 44)( 21, 43)( 22, 42)( 23, 41)( 24, 40)( 25, 39)
( 26, 38)( 27, 37)( 28, 36)( 29, 35)( 30, 34)( 31, 33)( 62, 63)( 64,122)
( 65,121)( 66,120)( 67,119)( 68,118)( 69,117)( 70,116)( 71,115)( 72,114)
( 73,113)( 74,112)( 75,111)( 76,110)( 77,109)( 78,108)( 79,107)( 80,106)
( 81,105)( 82,104)( 83,103)( 84,102)( 85,101)( 86,100)( 87, 99)( 88, 98)
( 89, 97)( 90, 96)( 91, 95)( 92, 94)(123,185)(124,184)(125,244)(126,243)
(127,242)(128,241)(129,240)(130,239)(131,238)(132,237)(133,236)(134,235)
(135,234)(136,233)(137,232)(138,231)(139,230)(140,229)(141,228)(142,227)
(143,226)(144,225)(145,224)(146,223)(147,222)(148,221)(149,220)(150,219)
(151,218)(152,217)(153,216)(154,215)(155,214)(156,213)(157,212)(158,211)
(159,210)(160,209)(161,208)(162,207)(163,206)(164,205)(165,204)(166,203)
(167,202)(168,201)(169,200)(170,199)(171,198)(172,197)(173,196)(174,195)
(175,194)(176,193)(177,192)(178,191)(179,190)(180,189)(181,188)(182,187)
(183,186);;
s2 := (  1,123)(  2,124)(  3,125)(  4,126)(  5,127)(  6,128)(  7,129)(  8,130)
(  9,131)( 10,132)( 11,133)( 12,134)( 13,135)( 14,136)( 15,137)( 16,138)
( 17,139)( 18,140)( 19,141)( 20,142)( 21,143)( 22,144)( 23,145)( 24,146)
( 25,147)( 26,148)( 27,149)( 28,150)( 29,151)( 30,152)( 31,153)( 32,154)
( 33,155)( 34,156)( 35,157)( 36,158)( 37,159)( 38,160)( 39,161)( 40,162)
( 41,163)( 42,164)( 43,165)( 44,166)( 45,167)( 46,168)( 47,169)( 48,170)
( 49,171)( 50,172)( 51,173)( 52,174)( 53,175)( 54,176)( 55,177)( 56,178)
( 57,179)( 58,180)( 59,181)( 60,182)( 61,183)( 62,184)( 63,185)( 64,186)
( 65,187)( 66,188)( 67,189)( 68,190)( 69,191)( 70,192)( 71,193)( 72,194)
( 73,195)( 74,196)( 75,197)( 76,198)( 77,199)( 78,200)( 79,201)( 80,202)
( 81,203)( 82,204)( 83,205)( 84,206)( 85,207)( 86,208)( 87,209)( 88,210)
( 89,211)( 90,212)( 91,213)( 92,214)( 93,215)( 94,216)( 95,217)( 96,218)
( 97,219)( 98,220)( 99,221)(100,222)(101,223)(102,224)(103,225)(104,226)
(105,227)(106,228)(107,229)(108,230)(109,231)(110,232)(111,233)(112,234)
(113,235)(114,236)(115,237)(116,238)(117,239)(118,240)(119,241)(120,242)
(121,243)(122,244);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(244)!(  2, 61)(  3, 60)(  4, 59)(  5, 58)(  6, 57)(  7, 56)(  8, 55)
(  9, 54)( 10, 53)( 11, 52)( 12, 51)( 13, 50)( 14, 49)( 15, 48)( 16, 47)
( 17, 46)( 18, 45)( 19, 44)( 20, 43)( 21, 42)( 22, 41)( 23, 40)( 24, 39)
( 25, 38)( 26, 37)( 27, 36)( 28, 35)( 29, 34)( 30, 33)( 31, 32)( 63,122)
( 64,121)( 65,120)( 66,119)( 67,118)( 68,117)( 69,116)( 70,115)( 71,114)
( 72,113)( 73,112)( 74,111)( 75,110)( 76,109)( 77,108)( 78,107)( 79,106)
( 80,105)( 81,104)( 82,103)( 83,102)( 84,101)( 85,100)( 86, 99)( 87, 98)
( 88, 97)( 89, 96)( 90, 95)( 91, 94)( 92, 93)(124,183)(125,182)(126,181)
(127,180)(128,179)(129,178)(130,177)(131,176)(132,175)(133,174)(134,173)
(135,172)(136,171)(137,170)(138,169)(139,168)(140,167)(141,166)(142,165)
(143,164)(144,163)(145,162)(146,161)(147,160)(148,159)(149,158)(150,157)
(151,156)(152,155)(153,154)(185,244)(186,243)(187,242)(188,241)(189,240)
(190,239)(191,238)(192,237)(193,236)(194,235)(195,234)(196,233)(197,232)
(198,231)(199,230)(200,229)(201,228)(202,227)(203,226)(204,225)(205,224)
(206,223)(207,222)(208,221)(209,220)(210,219)(211,218)(212,217)(213,216)
(214,215);
s1 := Sym(244)!(  1,  2)(  3, 61)(  4, 60)(  5, 59)(  6, 58)(  7, 57)(  8, 56)
(  9, 55)( 10, 54)( 11, 53)( 12, 52)( 13, 51)( 14, 50)( 15, 49)( 16, 48)
( 17, 47)( 18, 46)( 19, 45)( 20, 44)( 21, 43)( 22, 42)( 23, 41)( 24, 40)
( 25, 39)( 26, 38)( 27, 37)( 28, 36)( 29, 35)( 30, 34)( 31, 33)( 62, 63)
( 64,122)( 65,121)( 66,120)( 67,119)( 68,118)( 69,117)( 70,116)( 71,115)
( 72,114)( 73,113)( 74,112)( 75,111)( 76,110)( 77,109)( 78,108)( 79,107)
( 80,106)( 81,105)( 82,104)( 83,103)( 84,102)( 85,101)( 86,100)( 87, 99)
( 88, 98)( 89, 97)( 90, 96)( 91, 95)( 92, 94)(123,185)(124,184)(125,244)
(126,243)(127,242)(128,241)(129,240)(130,239)(131,238)(132,237)(133,236)
(134,235)(135,234)(136,233)(137,232)(138,231)(139,230)(140,229)(141,228)
(142,227)(143,226)(144,225)(145,224)(146,223)(147,222)(148,221)(149,220)
(150,219)(151,218)(152,217)(153,216)(154,215)(155,214)(156,213)(157,212)
(158,211)(159,210)(160,209)(161,208)(162,207)(163,206)(164,205)(165,204)
(166,203)(167,202)(168,201)(169,200)(170,199)(171,198)(172,197)(173,196)
(174,195)(175,194)(176,193)(177,192)(178,191)(179,190)(180,189)(181,188)
(182,187)(183,186);
s2 := Sym(244)!(  1,123)(  2,124)(  3,125)(  4,126)(  5,127)(  6,128)(  7,129)
(  8,130)(  9,131)( 10,132)( 11,133)( 12,134)( 13,135)( 14,136)( 15,137)
( 16,138)( 17,139)( 18,140)( 19,141)( 20,142)( 21,143)( 22,144)( 23,145)
( 24,146)( 25,147)( 26,148)( 27,149)( 28,150)( 29,151)( 30,152)( 31,153)
( 32,154)( 33,155)( 34,156)( 35,157)( 36,158)( 37,159)( 38,160)( 39,161)
( 40,162)( 41,163)( 42,164)( 43,165)( 44,166)( 45,167)( 46,168)( 47,169)
( 48,170)( 49,171)( 50,172)( 51,173)( 52,174)( 53,175)( 54,176)( 55,177)
( 56,178)( 57,179)( 58,180)( 59,181)( 60,182)( 61,183)( 62,184)( 63,185)
( 64,186)( 65,187)( 66,188)( 67,189)( 68,190)( 69,191)( 70,192)( 71,193)
( 72,194)( 73,195)( 74,196)( 75,197)( 76,198)( 77,199)( 78,200)( 79,201)
( 80,202)( 81,203)( 82,204)( 83,205)( 84,206)( 85,207)( 86,208)( 87,209)
( 88,210)( 89,211)( 90,212)( 91,213)( 92,214)( 93,215)( 94,216)( 95,217)
( 96,218)( 97,219)( 98,220)( 99,221)(100,222)(101,223)(102,224)(103,225)
(104,226)(105,227)(106,228)(107,229)(108,230)(109,231)(110,232)(111,233)
(112,234)(113,235)(114,236)(115,237)(116,238)(117,239)(118,240)(119,241)
(120,242)(121,243)(122,244);
poly := sub<Sym(244)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

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

References : None.
to this polytope