Polytope of Type {2,122,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,122,4}*1952
if this polytope has a name.
Group : SmallGroup(1952,182)
Rank : 4
Schlafli Type : {2,122,4}
Number of vertices, edges, etc : 2, 122, 244, 4
Order of s₀s₁s₂s₃ : 244
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 : {2,122,2}*976
   4-fold quotients : {2,61,2}*488
   61-fold quotients : {2,2,4}*32
   122-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 63)(  5, 62)(  6, 61)(  7, 60)(  8, 59)(  9, 58)( 10, 57)( 11, 56)
( 12, 55)( 13, 54)( 14, 53)( 15, 52)( 16, 51)( 17, 50)( 18, 49)( 19, 48)
( 20, 47)( 21, 46)( 22, 45)( 23, 44)( 24, 43)( 25, 42)( 26, 41)( 27, 40)
( 28, 39)( 29, 38)( 30, 37)( 31, 36)( 32, 35)( 33, 34)( 65,124)( 66,123)
( 67,122)( 68,121)( 69,120)( 70,119)( 71,118)( 72,117)( 73,116)( 74,115)
( 75,114)( 76,113)( 77,112)( 78,111)( 79,110)( 80,109)( 81,108)( 82,107)
( 83,106)( 84,105)( 85,104)( 86,103)( 87,102)( 88,101)( 89,100)( 90, 99)
( 91, 98)( 92, 97)( 93, 96)( 94, 95)(126,185)(127,184)(128,183)(129,182)
(130,181)(131,180)(132,179)(133,178)(134,177)(135,176)(136,175)(137,174)
(138,173)(139,172)(140,171)(141,170)(142,169)(143,168)(144,167)(145,166)
(146,165)(147,164)(148,163)(149,162)(150,161)(151,160)(152,159)(153,158)
(154,157)(155,156)(187,246)(188,245)(189,244)(190,243)(191,242)(192,241)
(193,240)(194,239)(195,238)(196,237)(197,236)(198,235)(199,234)(200,233)
(201,232)(202,231)(203,230)(204,229)(205,228)(206,227)(207,226)(208,225)
(209,224)(210,223)(211,222)(212,221)(213,220)(214,219)(215,218)(216,217);;
s2 := (  3,  4)(  5, 63)(  6, 62)(  7, 61)(  8, 60)(  9, 59)( 10, 58)( 11, 57)
( 12, 56)( 13, 55)( 14, 54)( 15, 53)( 16, 52)( 17, 51)( 18, 50)( 19, 49)
( 20, 48)( 21, 47)( 22, 46)( 23, 45)( 24, 44)( 25, 43)( 26, 42)( 27, 41)
( 28, 40)( 29, 39)( 30, 38)( 31, 37)( 32, 36)( 33, 35)( 64, 65)( 66,124)
( 67,123)( 68,122)( 69,121)( 70,120)( 71,119)( 72,118)( 73,117)( 74,116)
( 75,115)( 76,114)( 77,113)( 78,112)( 79,111)( 80,110)( 81,109)( 82,108)
( 83,107)( 84,106)( 85,105)( 86,104)( 87,103)( 88,102)( 89,101)( 90,100)
( 91, 99)( 92, 98)( 93, 97)( 94, 96)(125,187)(126,186)(127,246)(128,245)
(129,244)(130,243)(131,242)(132,241)(133,240)(134,239)(135,238)(136,237)
(137,236)(138,235)(139,234)(140,233)(141,232)(142,231)(143,230)(144,229)
(145,228)(146,227)(147,226)(148,225)(149,224)(150,223)(151,222)(152,221)
(153,220)(154,219)(155,218)(156,217)(157,216)(158,215)(159,214)(160,213)
(161,212)(162,211)(163,210)(164,209)(165,208)(166,207)(167,206)(168,205)
(169,204)(170,203)(171,202)(172,201)(173,200)(174,199)(175,198)(176,197)
(177,196)(178,195)(179,194)(180,193)(181,192)(182,191)(183,190)(184,189)
(185,188);;
s3 := (  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)
(123,245)(124,246);;
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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(246)!(1,2);
s1 := Sym(246)!(  4, 63)(  5, 62)(  6, 61)(  7, 60)(  8, 59)(  9, 58)( 10, 57)
( 11, 56)( 12, 55)( 13, 54)( 14, 53)( 15, 52)( 16, 51)( 17, 50)( 18, 49)
( 19, 48)( 20, 47)( 21, 46)( 22, 45)( 23, 44)( 24, 43)( 25, 42)( 26, 41)
( 27, 40)( 28, 39)( 29, 38)( 30, 37)( 31, 36)( 32, 35)( 33, 34)( 65,124)
( 66,123)( 67,122)( 68,121)( 69,120)( 70,119)( 71,118)( 72,117)( 73,116)
( 74,115)( 75,114)( 76,113)( 77,112)( 78,111)( 79,110)( 80,109)( 81,108)
( 82,107)( 83,106)( 84,105)( 85,104)( 86,103)( 87,102)( 88,101)( 89,100)
( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)(126,185)(127,184)(128,183)
(129,182)(130,181)(131,180)(132,179)(133,178)(134,177)(135,176)(136,175)
(137,174)(138,173)(139,172)(140,171)(141,170)(142,169)(143,168)(144,167)
(145,166)(146,165)(147,164)(148,163)(149,162)(150,161)(151,160)(152,159)
(153,158)(154,157)(155,156)(187,246)(188,245)(189,244)(190,243)(191,242)
(192,241)(193,240)(194,239)(195,238)(196,237)(197,236)(198,235)(199,234)
(200,233)(201,232)(202,231)(203,230)(204,229)(205,228)(206,227)(207,226)
(208,225)(209,224)(210,223)(211,222)(212,221)(213,220)(214,219)(215,218)
(216,217);
s2 := Sym(246)!(  3,  4)(  5, 63)(  6, 62)(  7, 61)(  8, 60)(  9, 59)( 10, 58)
( 11, 57)( 12, 56)( 13, 55)( 14, 54)( 15, 53)( 16, 52)( 17, 51)( 18, 50)
( 19, 49)( 20, 48)( 21, 47)( 22, 46)( 23, 45)( 24, 44)( 25, 43)( 26, 42)
( 27, 41)( 28, 40)( 29, 39)( 30, 38)( 31, 37)( 32, 36)( 33, 35)( 64, 65)
( 66,124)( 67,123)( 68,122)( 69,121)( 70,120)( 71,119)( 72,118)( 73,117)
( 74,116)( 75,115)( 76,114)( 77,113)( 78,112)( 79,111)( 80,110)( 81,109)
( 82,108)( 83,107)( 84,106)( 85,105)( 86,104)( 87,103)( 88,102)( 89,101)
( 90,100)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(125,187)(126,186)(127,246)
(128,245)(129,244)(130,243)(131,242)(132,241)(133,240)(134,239)(135,238)
(136,237)(137,236)(138,235)(139,234)(140,233)(141,232)(142,231)(143,230)
(144,229)(145,228)(146,227)(147,226)(148,225)(149,224)(150,223)(151,222)
(152,221)(153,220)(154,219)(155,218)(156,217)(157,216)(158,215)(159,214)
(160,213)(161,212)(162,211)(163,210)(164,209)(165,208)(166,207)(167,206)
(168,205)(169,204)(170,203)(171,202)(172,201)(173,200)(174,199)(175,198)
(176,197)(177,196)(178,195)(179,194)(180,193)(181,192)(182,191)(183,190)
(184,189)(185,188);
s3 := Sym(246)!(  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)(123,245)(124,246);
poly := sub<Sym(246)|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*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope