Polytope of Type {4,124}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,124}*1984
if this polytope has a name.
Group : SmallGroup(1984,737)
Rank : 3
Schlafli Type : {4,124}
Number of vertices, edges, etc : 8, 496, 248
Order of s₀s₁s₂ : 124
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {4,124}*992
   4-fold quotients : {2,124}*496, {4,62}*496
   8-fold quotients : {2,62}*248
   16-fold quotients : {2,31}*124
   31-fold quotients : {4,4}*64
   62-fold quotients : {4,4}*32
   124-fold quotients : {2,4}*16, {4,2}*16
   248-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

References : None.
to this polytope