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Polytope of Type {2,63,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,63,4}*1008
if this polytope has a name.
Group : SmallGroup(1008,503)
Rank : 4
Schlafli Type : {2,63,4}
Number of vertices, edges, etc : 2, 63, 126, 4
Order of s0s1s2s3 : 126
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-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) :
   3-fold quotients : {2,21,4}*336
   7-fold quotients : {2,9,4}*144
   21-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  4,  5)(  7, 11)(  8, 13)(  9, 12)( 10, 14)( 15, 75)( 16, 77)( 17, 76)
( 18, 78)( 19, 83)( 20, 85)( 21, 84)( 22, 86)( 23, 79)( 24, 81)( 25, 80)
( 26, 82)( 27, 63)( 28, 65)( 29, 64)( 30, 66)( 31, 71)( 32, 73)( 33, 72)
( 34, 74)( 35, 67)( 36, 69)( 37, 68)( 38, 70)( 39, 51)( 40, 53)( 41, 52)
( 42, 54)( 43, 59)( 44, 61)( 45, 60)( 46, 62)( 47, 55)( 48, 57)( 49, 56)
( 50, 58)( 87,175)( 88,177)( 89,176)( 90,178)( 91,171)( 92,173)( 93,172)
( 94,174)( 95,179)( 96,181)( 97,180)( 98,182)( 99,247)(100,249)(101,248)
(102,250)(103,243)(104,245)(105,244)(106,246)(107,251)(108,253)(109,252)
(110,254)(111,235)(112,237)(113,236)(114,238)(115,231)(116,233)(117,232)
(118,234)(119,239)(120,241)(121,240)(122,242)(123,223)(124,225)(125,224)
(126,226)(127,219)(128,221)(129,220)(130,222)(131,227)(132,229)(133,228)
(134,230)(135,211)(136,213)(137,212)(138,214)(139,207)(140,209)(141,208)
(142,210)(143,215)(144,217)(145,216)(146,218)(147,199)(148,201)(149,200)
(150,202)(151,195)(152,197)(153,196)(154,198)(155,203)(156,205)(157,204)
(158,206)(159,187)(160,189)(161,188)(162,190)(163,183)(164,185)(165,184)
(166,186)(167,191)(168,193)(169,192)(170,194);;
s2 := (  3, 99)(  4,100)(  5,102)(  6,101)(  7,107)(  8,108)(  9,110)( 10,109)
( 11,103)( 12,104)( 13,106)( 14,105)( 15, 87)( 16, 88)( 17, 90)( 18, 89)
( 19, 95)( 20, 96)( 21, 98)( 22, 97)( 23, 91)( 24, 92)( 25, 94)( 26, 93)
( 27,159)( 28,160)( 29,162)( 30,161)( 31,167)( 32,168)( 33,170)( 34,169)
( 35,163)( 36,164)( 37,166)( 38,165)( 39,147)( 40,148)( 41,150)( 42,149)
( 43,155)( 44,156)( 45,158)( 46,157)( 47,151)( 48,152)( 49,154)( 50,153)
( 51,135)( 52,136)( 53,138)( 54,137)( 55,143)( 56,144)( 57,146)( 58,145)
( 59,139)( 60,140)( 61,142)( 62,141)( 63,123)( 64,124)( 65,126)( 66,125)
( 67,131)( 68,132)( 69,134)( 70,133)( 71,127)( 72,128)( 73,130)( 74,129)
( 75,111)( 76,112)( 77,114)( 78,113)( 79,119)( 80,120)( 81,122)( 82,121)
( 83,115)( 84,116)( 85,118)( 86,117)(171,187)(172,188)(173,190)(174,189)
(175,183)(176,184)(177,186)(178,185)(179,191)(180,192)(181,194)(182,193)
(195,247)(196,248)(197,250)(198,249)(199,243)(200,244)(201,246)(202,245)
(203,251)(204,252)(205,254)(206,253)(207,235)(208,236)(209,238)(210,237)
(211,231)(212,232)(213,234)(214,233)(215,239)(216,240)(217,242)(218,241)
(219,223)(220,224)(221,226)(222,225)(229,230);;
s3 := (  3,  6)(  4,  5)(  7, 10)(  8,  9)( 11, 14)( 12, 13)( 15, 18)( 16, 17)
( 19, 22)( 20, 21)( 23, 26)( 24, 25)( 27, 30)( 28, 29)( 31, 34)( 32, 33)
( 35, 38)( 36, 37)( 39, 42)( 40, 41)( 43, 46)( 44, 45)( 47, 50)( 48, 49)
( 51, 54)( 52, 53)( 55, 58)( 56, 57)( 59, 62)( 60, 61)( 63, 66)( 64, 65)
( 67, 70)( 68, 69)( 71, 74)( 72, 73)( 75, 78)( 76, 77)( 79, 82)( 80, 81)
( 83, 86)( 84, 85)( 87, 90)( 88, 89)( 91, 94)( 92, 93)( 95, 98)( 96, 97)
( 99,102)(100,101)(103,106)(104,105)(107,110)(108,109)(111,114)(112,113)
(115,118)(116,117)(119,122)(120,121)(123,126)(124,125)(127,130)(128,129)
(131,134)(132,133)(135,138)(136,137)(139,142)(140,141)(143,146)(144,145)
(147,150)(148,149)(151,154)(152,153)(155,158)(156,157)(159,162)(160,161)
(163,166)(164,165)(167,170)(168,169)(171,174)(172,173)(175,178)(176,177)
(179,182)(180,181)(183,186)(184,185)(187,190)(188,189)(191,194)(192,193)
(195,198)(196,197)(199,202)(200,201)(203,206)(204,205)(207,210)(208,209)
(211,214)(212,213)(215,218)(216,217)(219,222)(220,221)(223,226)(224,225)
(227,230)(228,229)(231,234)(232,233)(235,238)(236,237)(239,242)(240,241)
(243,246)(244,245)(247,250)(248,249)(251,254)(252,253);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(254)!(1,2);
s1 := Sym(254)!(  4,  5)(  7, 11)(  8, 13)(  9, 12)( 10, 14)( 15, 75)( 16, 77)
( 17, 76)( 18, 78)( 19, 83)( 20, 85)( 21, 84)( 22, 86)( 23, 79)( 24, 81)
( 25, 80)( 26, 82)( 27, 63)( 28, 65)( 29, 64)( 30, 66)( 31, 71)( 32, 73)
( 33, 72)( 34, 74)( 35, 67)( 36, 69)( 37, 68)( 38, 70)( 39, 51)( 40, 53)
( 41, 52)( 42, 54)( 43, 59)( 44, 61)( 45, 60)( 46, 62)( 47, 55)( 48, 57)
( 49, 56)( 50, 58)( 87,175)( 88,177)( 89,176)( 90,178)( 91,171)( 92,173)
( 93,172)( 94,174)( 95,179)( 96,181)( 97,180)( 98,182)( 99,247)(100,249)
(101,248)(102,250)(103,243)(104,245)(105,244)(106,246)(107,251)(108,253)
(109,252)(110,254)(111,235)(112,237)(113,236)(114,238)(115,231)(116,233)
(117,232)(118,234)(119,239)(120,241)(121,240)(122,242)(123,223)(124,225)
(125,224)(126,226)(127,219)(128,221)(129,220)(130,222)(131,227)(132,229)
(133,228)(134,230)(135,211)(136,213)(137,212)(138,214)(139,207)(140,209)
(141,208)(142,210)(143,215)(144,217)(145,216)(146,218)(147,199)(148,201)
(149,200)(150,202)(151,195)(152,197)(153,196)(154,198)(155,203)(156,205)
(157,204)(158,206)(159,187)(160,189)(161,188)(162,190)(163,183)(164,185)
(165,184)(166,186)(167,191)(168,193)(169,192)(170,194);
s2 := Sym(254)!(  3, 99)(  4,100)(  5,102)(  6,101)(  7,107)(  8,108)(  9,110)
( 10,109)( 11,103)( 12,104)( 13,106)( 14,105)( 15, 87)( 16, 88)( 17, 90)
( 18, 89)( 19, 95)( 20, 96)( 21, 98)( 22, 97)( 23, 91)( 24, 92)( 25, 94)
( 26, 93)( 27,159)( 28,160)( 29,162)( 30,161)( 31,167)( 32,168)( 33,170)
( 34,169)( 35,163)( 36,164)( 37,166)( 38,165)( 39,147)( 40,148)( 41,150)
( 42,149)( 43,155)( 44,156)( 45,158)( 46,157)( 47,151)( 48,152)( 49,154)
( 50,153)( 51,135)( 52,136)( 53,138)( 54,137)( 55,143)( 56,144)( 57,146)
( 58,145)( 59,139)( 60,140)( 61,142)( 62,141)( 63,123)( 64,124)( 65,126)
( 66,125)( 67,131)( 68,132)( 69,134)( 70,133)( 71,127)( 72,128)( 73,130)
( 74,129)( 75,111)( 76,112)( 77,114)( 78,113)( 79,119)( 80,120)( 81,122)
( 82,121)( 83,115)( 84,116)( 85,118)( 86,117)(171,187)(172,188)(173,190)
(174,189)(175,183)(176,184)(177,186)(178,185)(179,191)(180,192)(181,194)
(182,193)(195,247)(196,248)(197,250)(198,249)(199,243)(200,244)(201,246)
(202,245)(203,251)(204,252)(205,254)(206,253)(207,235)(208,236)(209,238)
(210,237)(211,231)(212,232)(213,234)(214,233)(215,239)(216,240)(217,242)
(218,241)(219,223)(220,224)(221,226)(222,225)(229,230);
s3 := Sym(254)!(  3,  6)(  4,  5)(  7, 10)(  8,  9)( 11, 14)( 12, 13)( 15, 18)
( 16, 17)( 19, 22)( 20, 21)( 23, 26)( 24, 25)( 27, 30)( 28, 29)( 31, 34)
( 32, 33)( 35, 38)( 36, 37)( 39, 42)( 40, 41)( 43, 46)( 44, 45)( 47, 50)
( 48, 49)( 51, 54)( 52, 53)( 55, 58)( 56, 57)( 59, 62)( 60, 61)( 63, 66)
( 64, 65)( 67, 70)( 68, 69)( 71, 74)( 72, 73)( 75, 78)( 76, 77)( 79, 82)
( 80, 81)( 83, 86)( 84, 85)( 87, 90)( 88, 89)( 91, 94)( 92, 93)( 95, 98)
( 96, 97)( 99,102)(100,101)(103,106)(104,105)(107,110)(108,109)(111,114)
(112,113)(115,118)(116,117)(119,122)(120,121)(123,126)(124,125)(127,130)
(128,129)(131,134)(132,133)(135,138)(136,137)(139,142)(140,141)(143,146)
(144,145)(147,150)(148,149)(151,154)(152,153)(155,158)(156,157)(159,162)
(160,161)(163,166)(164,165)(167,170)(168,169)(171,174)(172,173)(175,178)
(176,177)(179,182)(180,181)(183,186)(184,185)(187,190)(188,189)(191,194)
(192,193)(195,198)(196,197)(199,202)(200,201)(203,206)(204,205)(207,210)
(208,209)(211,214)(212,213)(215,218)(216,217)(219,222)(220,221)(223,226)
(224,225)(227,230)(228,229)(231,234)(232,233)(235,238)(236,237)(239,242)
(240,241)(243,246)(244,245)(247,250)(248,249)(251,254)(252,253);
poly := sub<Sym(254)|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, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s2*s1*s3*s2*s3*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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