Polytope of Type {2,124,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,124,4}*1984
if this polytope has a name.
Group : SmallGroup(1984,1036)
Rank : 4
Schlafli Type : {2,124,4}
Number of vertices, edges, etc : 2, 124, 248, 4
Order of s₀s₁s₂s₃ : 124
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 : {2,124,2}*992, {2,62,4}*992
   4-fold quotients : {2,62,2}*496
   8-fold quotients : {2,31,2}*248
   31-fold quotients : {2,4,4}*64
   62-fold quotients : {2,2,4}*32, {2,4,2}*32
   124-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 33)(  5, 32)(  6, 31)(  7, 30)(  8, 29)(  9, 28)( 10, 27)( 11, 26)
( 12, 25)( 13, 24)( 14, 23)( 15, 22)( 16, 21)( 17, 20)( 18, 19)( 35, 64)
( 36, 63)( 37, 62)( 38, 61)( 39, 60)( 40, 59)( 41, 58)( 42, 57)( 43, 56)
( 44, 55)( 45, 54)( 46, 53)( 47, 52)( 48, 51)( 49, 50)( 66, 95)( 67, 94)
( 68, 93)( 69, 92)( 70, 91)( 71, 90)( 72, 89)( 73, 88)( 74, 87)( 75, 86)
( 76, 85)( 77, 84)( 78, 83)( 79, 82)( 80, 81)( 97,126)( 98,125)( 99,124)
(100,123)(101,122)(102,121)(103,120)(104,119)(105,118)(106,117)(107,116)
(108,115)(109,114)(110,113)(111,112)(127,189)(128,219)(129,218)(130,217)
(131,216)(132,215)(133,214)(134,213)(135,212)(136,211)(137,210)(138,209)
(139,208)(140,207)(141,206)(142,205)(143,204)(144,203)(145,202)(146,201)
(147,200)(148,199)(149,198)(150,197)(151,196)(152,195)(153,194)(154,193)
(155,192)(156,191)(157,190)(158,220)(159,250)(160,249)(161,248)(162,247)
(163,246)(164,245)(165,244)(166,243)(167,242)(168,241)(169,240)(170,239)
(171,238)(172,237)(173,236)(174,235)(175,234)(176,233)(177,232)(178,231)
(179,230)(180,229)(181,228)(182,227)(183,226)(184,225)(185,224)(186,223)
(187,222)(188,221);;
s2 := (  3,128)(  4,127)(  5,157)(  6,156)(  7,155)(  8,154)(  9,153)( 10,152)
( 11,151)( 12,150)( 13,149)( 14,148)( 15,147)( 16,146)( 17,145)( 18,144)
( 19,143)( 20,142)( 21,141)( 22,140)( 23,139)( 24,138)( 25,137)( 26,136)
( 27,135)( 28,134)( 29,133)( 30,132)( 31,131)( 32,130)( 33,129)( 34,159)
( 35,158)( 36,188)( 37,187)( 38,186)( 39,185)( 40,184)( 41,183)( 42,182)
( 43,181)( 44,180)( 45,179)( 46,178)( 47,177)( 48,176)( 49,175)( 50,174)
( 51,173)( 52,172)( 53,171)( 54,170)( 55,169)( 56,168)( 57,167)( 58,166)
( 59,165)( 60,164)( 61,163)( 62,162)( 63,161)( 64,160)( 65,190)( 66,189)
( 67,219)( 68,218)( 69,217)( 70,216)( 71,215)( 72,214)( 73,213)( 74,212)
( 75,211)( 76,210)( 77,209)( 78,208)( 79,207)( 80,206)( 81,205)( 82,204)
( 83,203)( 84,202)( 85,201)( 86,200)( 87,199)( 88,198)( 89,197)( 90,196)
( 91,195)( 92,194)( 93,193)( 94,192)( 95,191)( 96,221)( 97,220)( 98,250)
( 99,249)(100,248)(101,247)(102,246)(103,245)(104,244)(105,243)(106,242)
(107,241)(108,240)(109,239)(110,238)(111,237)(112,236)(113,235)(114,234)
(115,233)(116,232)(117,231)(118,230)(119,229)(120,228)(121,227)(122,226)
(123,225)(124,224)(125,223)(126,222);;
s3 := (127,158)(128,159)(129,160)(130,161)(131,162)(132,163)(133,164)(134,165)
(135,166)(136,167)(137,168)(138,169)(139,170)(140,171)(141,172)(142,173)
(143,174)(144,175)(145,176)(146,177)(147,178)(148,179)(149,180)(150,181)
(151,182)(152,183)(153,184)(154,185)(155,186)(156,187)(157,188)(189,220)
(190,221)(191,222)(192,223)(193,224)(194,225)(195,226)(196,227)(197,228)
(198,229)(199,230)(200,231)(201,232)(202,233)(203,234)(204,235)(205,236)
(206,237)(207,238)(208,239)(209,240)(210,241)(211,242)(212,243)(213,244)
(214,245)(215,246)(216,247)(217,248)(218,249)(219,250);;
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*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(250)!(1,2);
s1 := Sym(250)!(  4, 33)(  5, 32)(  6, 31)(  7, 30)(  8, 29)(  9, 28)( 10, 27)
( 11, 26)( 12, 25)( 13, 24)( 14, 23)( 15, 22)( 16, 21)( 17, 20)( 18, 19)
( 35, 64)( 36, 63)( 37, 62)( 38, 61)( 39, 60)( 40, 59)( 41, 58)( 42, 57)
( 43, 56)( 44, 55)( 45, 54)( 46, 53)( 47, 52)( 48, 51)( 49, 50)( 66, 95)
( 67, 94)( 68, 93)( 69, 92)( 70, 91)( 71, 90)( 72, 89)( 73, 88)( 74, 87)
( 75, 86)( 76, 85)( 77, 84)( 78, 83)( 79, 82)( 80, 81)( 97,126)( 98,125)
( 99,124)(100,123)(101,122)(102,121)(103,120)(104,119)(105,118)(106,117)
(107,116)(108,115)(109,114)(110,113)(111,112)(127,189)(128,219)(129,218)
(130,217)(131,216)(132,215)(133,214)(134,213)(135,212)(136,211)(137,210)
(138,209)(139,208)(140,207)(141,206)(142,205)(143,204)(144,203)(145,202)
(146,201)(147,200)(148,199)(149,198)(150,197)(151,196)(152,195)(153,194)
(154,193)(155,192)(156,191)(157,190)(158,220)(159,250)(160,249)(161,248)
(162,247)(163,246)(164,245)(165,244)(166,243)(167,242)(168,241)(169,240)
(170,239)(171,238)(172,237)(173,236)(174,235)(175,234)(176,233)(177,232)
(178,231)(179,230)(180,229)(181,228)(182,227)(183,226)(184,225)(185,224)
(186,223)(187,222)(188,221);
s2 := Sym(250)!(  3,128)(  4,127)(  5,157)(  6,156)(  7,155)(  8,154)(  9,153)
( 10,152)( 11,151)( 12,150)( 13,149)( 14,148)( 15,147)( 16,146)( 17,145)
( 18,144)( 19,143)( 20,142)( 21,141)( 22,140)( 23,139)( 24,138)( 25,137)
( 26,136)( 27,135)( 28,134)( 29,133)( 30,132)( 31,131)( 32,130)( 33,129)
( 34,159)( 35,158)( 36,188)( 37,187)( 38,186)( 39,185)( 40,184)( 41,183)
( 42,182)( 43,181)( 44,180)( 45,179)( 46,178)( 47,177)( 48,176)( 49,175)
( 50,174)( 51,173)( 52,172)( 53,171)( 54,170)( 55,169)( 56,168)( 57,167)
( 58,166)( 59,165)( 60,164)( 61,163)( 62,162)( 63,161)( 64,160)( 65,190)
( 66,189)( 67,219)( 68,218)( 69,217)( 70,216)( 71,215)( 72,214)( 73,213)
( 74,212)( 75,211)( 76,210)( 77,209)( 78,208)( 79,207)( 80,206)( 81,205)
( 82,204)( 83,203)( 84,202)( 85,201)( 86,200)( 87,199)( 88,198)( 89,197)
( 90,196)( 91,195)( 92,194)( 93,193)( 94,192)( 95,191)( 96,221)( 97,220)
( 98,250)( 99,249)(100,248)(101,247)(102,246)(103,245)(104,244)(105,243)
(106,242)(107,241)(108,240)(109,239)(110,238)(111,237)(112,236)(113,235)
(114,234)(115,233)(116,232)(117,231)(118,230)(119,229)(120,228)(121,227)
(122,226)(123,225)(124,224)(125,223)(126,222);
s3 := Sym(250)!(127,158)(128,159)(129,160)(130,161)(131,162)(132,163)(133,164)
(134,165)(135,166)(136,167)(137,168)(138,169)(139,170)(140,171)(141,172)
(142,173)(143,174)(144,175)(145,176)(146,177)(147,178)(148,179)(149,180)
(150,181)(151,182)(152,183)(153,184)(154,185)(155,186)(156,187)(157,188)
(189,220)(190,221)(191,222)(192,223)(193,224)(194,225)(195,226)(196,227)
(197,228)(198,229)(199,230)(200,231)(201,232)(202,233)(203,234)(204,235)
(205,236)(206,237)(207,238)(208,239)(209,240)(210,241)(211,242)(212,243)
(213,244)(214,245)(215,246)(216,247)(217,248)(218,249)(219,250);
poly := sub<Sym(250)|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*s1*s2*s1*s2 >;

to this polytope