Questions?
See the FAQ
or other info.

Polytope of Type {4,126}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,126}*1008c
if this polytope has a name.
Group : SmallGroup(1008,503)
Rank : 3
Schlafli Type : {4,126}
Number of vertices, edges, etc : 4, 252, 126
Order of s0s1s2 : 63
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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) :
   2-fold quotients : {4,63}*504
   3-fold quotients : {4,42}*336c
   6-fold quotients : {4,21}*168
   7-fold quotients : {4,18}*144c
   14-fold quotients : {4,9}*72
   21-fold quotients : {4,6}*48b
   42-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,255)(  2,256)(  3,253)(  4,254)(  5,259)(  6,260)(  7,257)(  8,258)
(  9,263)( 10,264)( 11,261)( 12,262)( 13,267)( 14,268)( 15,265)( 16,266)
( 17,271)( 18,272)( 19,269)( 20,270)( 21,275)( 22,276)( 23,273)( 24,274)
( 25,279)( 26,280)( 27,277)( 28,278)( 29,283)( 30,284)( 31,281)( 32,282)
( 33,287)( 34,288)( 35,285)( 36,286)( 37,291)( 38,292)( 39,289)( 40,290)
( 41,295)( 42,296)( 43,293)( 44,294)( 45,299)( 46,300)( 47,297)( 48,298)
( 49,303)( 50,304)( 51,301)( 52,302)( 53,307)( 54,308)( 55,305)( 56,306)
( 57,311)( 58,312)( 59,309)( 60,310)( 61,315)( 62,316)( 63,313)( 64,314)
( 65,319)( 66,320)( 67,317)( 68,318)( 69,323)( 70,324)( 71,321)( 72,322)
( 73,327)( 74,328)( 75,325)( 76,326)( 77,331)( 78,332)( 79,329)( 80,330)
( 81,335)( 82,336)( 83,333)( 84,334)( 85,339)( 86,340)( 87,337)( 88,338)
( 89,343)( 90,344)( 91,341)( 92,342)( 93,347)( 94,348)( 95,345)( 96,346)
( 97,351)( 98,352)( 99,349)(100,350)(101,355)(102,356)(103,353)(104,354)
(105,359)(106,360)(107,357)(108,358)(109,363)(110,364)(111,361)(112,362)
(113,367)(114,368)(115,365)(116,366)(117,371)(118,372)(119,369)(120,370)
(121,375)(122,376)(123,373)(124,374)(125,379)(126,380)(127,377)(128,378)
(129,383)(130,384)(131,381)(132,382)(133,387)(134,388)(135,385)(136,386)
(137,391)(138,392)(139,389)(140,390)(141,395)(142,396)(143,393)(144,394)
(145,399)(146,400)(147,397)(148,398)(149,403)(150,404)(151,401)(152,402)
(153,407)(154,408)(155,405)(156,406)(157,411)(158,412)(159,409)(160,410)
(161,415)(162,416)(163,413)(164,414)(165,419)(166,420)(167,417)(168,418)
(169,423)(170,424)(171,421)(172,422)(173,427)(174,428)(175,425)(176,426)
(177,431)(178,432)(179,429)(180,430)(181,435)(182,436)(183,433)(184,434)
(185,439)(186,440)(187,437)(188,438)(189,443)(190,444)(191,441)(192,442)
(193,447)(194,448)(195,445)(196,446)(197,451)(198,452)(199,449)(200,450)
(201,455)(202,456)(203,453)(204,454)(205,459)(206,460)(207,457)(208,458)
(209,463)(210,464)(211,461)(212,462)(213,467)(214,468)(215,465)(216,466)
(217,471)(218,472)(219,469)(220,470)(221,475)(222,476)(223,473)(224,474)
(225,479)(226,480)(227,477)(228,478)(229,483)(230,484)(231,481)(232,482)
(233,487)(234,488)(235,485)(236,486)(237,491)(238,492)(239,489)(240,490)
(241,495)(242,496)(243,493)(244,494)(245,499)(246,500)(247,497)(248,498)
(249,503)(250,504)(251,501)(252,502);;
s1 := (  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 13, 73)( 14, 74)( 15, 76)
( 16, 75)( 17, 81)( 18, 82)( 19, 84)( 20, 83)( 21, 77)( 22, 78)( 23, 80)
( 24, 79)( 25, 61)( 26, 62)( 27, 64)( 28, 63)( 29, 69)( 30, 70)( 31, 72)
( 32, 71)( 33, 65)( 34, 66)( 35, 68)( 36, 67)( 37, 49)( 38, 50)( 39, 52)
( 40, 51)( 41, 57)( 42, 58)( 43, 60)( 44, 59)( 45, 53)( 46, 54)( 47, 56)
( 48, 55)( 85,177)( 86,178)( 87,180)( 88,179)( 89,173)( 90,174)( 91,176)
( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)( 97,249)( 98,250)( 99,252)
(100,251)(101,245)(102,246)(103,248)(104,247)(105,241)(106,242)(107,244)
(108,243)(109,237)(110,238)(111,240)(112,239)(113,233)(114,234)(115,236)
(116,235)(117,229)(118,230)(119,232)(120,231)(121,225)(122,226)(123,228)
(124,227)(125,221)(126,222)(127,224)(128,223)(129,217)(130,218)(131,220)
(132,219)(133,213)(134,214)(135,216)(136,215)(137,209)(138,210)(139,212)
(140,211)(141,205)(142,206)(143,208)(144,207)(145,201)(146,202)(147,204)
(148,203)(149,197)(150,198)(151,200)(152,199)(153,193)(154,194)(155,196)
(156,195)(157,189)(158,190)(159,192)(160,191)(161,185)(162,186)(163,188)
(164,187)(165,181)(166,182)(167,184)(168,183)(255,256)(257,261)(258,262)
(259,264)(260,263)(265,325)(266,326)(267,328)(268,327)(269,333)(270,334)
(271,336)(272,335)(273,329)(274,330)(275,332)(276,331)(277,313)(278,314)
(279,316)(280,315)(281,321)(282,322)(283,324)(284,323)(285,317)(286,318)
(287,320)(288,319)(289,301)(290,302)(291,304)(292,303)(293,309)(294,310)
(295,312)(296,311)(297,305)(298,306)(299,308)(300,307)(337,429)(338,430)
(339,432)(340,431)(341,425)(342,426)(343,428)(344,427)(345,421)(346,422)
(347,424)(348,423)(349,501)(350,502)(351,504)(352,503)(353,497)(354,498)
(355,500)(356,499)(357,493)(358,494)(359,496)(360,495)(361,489)(362,490)
(363,492)(364,491)(365,485)(366,486)(367,488)(368,487)(369,481)(370,482)
(371,484)(372,483)(373,477)(374,478)(375,480)(376,479)(377,473)(378,474)
(379,476)(380,475)(381,469)(382,470)(383,472)(384,471)(385,465)(386,466)
(387,468)(388,467)(389,461)(390,462)(391,464)(392,463)(393,457)(394,458)
(395,460)(396,459)(397,453)(398,454)(399,456)(400,455)(401,449)(402,450)
(403,452)(404,451)(405,445)(406,446)(407,448)(408,447)(409,441)(410,442)
(411,444)(412,443)(413,437)(414,438)(415,440)(416,439)(417,433)(418,434)
(419,436)(420,435);;
s2 := (  1,349)(  2,352)(  3,351)(  4,350)(  5,357)(  6,360)(  7,359)(  8,358)
(  9,353)( 10,356)( 11,355)( 12,354)( 13,337)( 14,340)( 15,339)( 16,338)
( 17,345)( 18,348)( 19,347)( 20,346)( 21,341)( 22,344)( 23,343)( 24,342)
( 25,409)( 26,412)( 27,411)( 28,410)( 29,417)( 30,420)( 31,419)( 32,418)
( 33,413)( 34,416)( 35,415)( 36,414)( 37,397)( 38,400)( 39,399)( 40,398)
( 41,405)( 42,408)( 43,407)( 44,406)( 45,401)( 46,404)( 47,403)( 48,402)
( 49,385)( 50,388)( 51,387)( 52,386)( 53,393)( 54,396)( 55,395)( 56,394)
( 57,389)( 58,392)( 59,391)( 60,390)( 61,373)( 62,376)( 63,375)( 64,374)
( 65,381)( 66,384)( 67,383)( 68,382)( 69,377)( 70,380)( 71,379)( 72,378)
( 73,361)( 74,364)( 75,363)( 76,362)( 77,369)( 78,372)( 79,371)( 80,370)
( 81,365)( 82,368)( 83,367)( 84,366)( 85,265)( 86,268)( 87,267)( 88,266)
( 89,273)( 90,276)( 91,275)( 92,274)( 93,269)( 94,272)( 95,271)( 96,270)
( 97,253)( 98,256)( 99,255)(100,254)(101,261)(102,264)(103,263)(104,262)
(105,257)(106,260)(107,259)(108,258)(109,325)(110,328)(111,327)(112,326)
(113,333)(114,336)(115,335)(116,334)(117,329)(118,332)(119,331)(120,330)
(121,313)(122,316)(123,315)(124,314)(125,321)(126,324)(127,323)(128,322)
(129,317)(130,320)(131,319)(132,318)(133,301)(134,304)(135,303)(136,302)
(137,309)(138,312)(139,311)(140,310)(141,305)(142,308)(143,307)(144,306)
(145,289)(146,292)(147,291)(148,290)(149,297)(150,300)(151,299)(152,298)
(153,293)(154,296)(155,295)(156,294)(157,277)(158,280)(159,279)(160,278)
(161,285)(162,288)(163,287)(164,286)(165,281)(166,284)(167,283)(168,282)
(169,441)(170,444)(171,443)(172,442)(173,437)(174,440)(175,439)(176,438)
(177,433)(178,436)(179,435)(180,434)(181,429)(182,432)(183,431)(184,430)
(185,425)(186,428)(187,427)(188,426)(189,421)(190,424)(191,423)(192,422)
(193,501)(194,504)(195,503)(196,502)(197,497)(198,500)(199,499)(200,498)
(201,493)(202,496)(203,495)(204,494)(205,489)(206,492)(207,491)(208,490)
(209,485)(210,488)(211,487)(212,486)(213,481)(214,484)(215,483)(216,482)
(217,477)(218,480)(219,479)(220,478)(221,473)(222,476)(223,475)(224,474)
(225,469)(226,472)(227,471)(228,470)(229,465)(230,468)(231,467)(232,466)
(233,461)(234,464)(235,463)(236,462)(237,457)(238,460)(239,459)(240,458)
(241,453)(242,456)(243,455)(244,454)(245,449)(246,452)(247,451)(248,450)
(249,445)(250,448)(251,447)(252,446);;
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, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*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*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(504)!(  1,255)(  2,256)(  3,253)(  4,254)(  5,259)(  6,260)(  7,257)
(  8,258)(  9,263)( 10,264)( 11,261)( 12,262)( 13,267)( 14,268)( 15,265)
( 16,266)( 17,271)( 18,272)( 19,269)( 20,270)( 21,275)( 22,276)( 23,273)
( 24,274)( 25,279)( 26,280)( 27,277)( 28,278)( 29,283)( 30,284)( 31,281)
( 32,282)( 33,287)( 34,288)( 35,285)( 36,286)( 37,291)( 38,292)( 39,289)
( 40,290)( 41,295)( 42,296)( 43,293)( 44,294)( 45,299)( 46,300)( 47,297)
( 48,298)( 49,303)( 50,304)( 51,301)( 52,302)( 53,307)( 54,308)( 55,305)
( 56,306)( 57,311)( 58,312)( 59,309)( 60,310)( 61,315)( 62,316)( 63,313)
( 64,314)( 65,319)( 66,320)( 67,317)( 68,318)( 69,323)( 70,324)( 71,321)
( 72,322)( 73,327)( 74,328)( 75,325)( 76,326)( 77,331)( 78,332)( 79,329)
( 80,330)( 81,335)( 82,336)( 83,333)( 84,334)( 85,339)( 86,340)( 87,337)
( 88,338)( 89,343)( 90,344)( 91,341)( 92,342)( 93,347)( 94,348)( 95,345)
( 96,346)( 97,351)( 98,352)( 99,349)(100,350)(101,355)(102,356)(103,353)
(104,354)(105,359)(106,360)(107,357)(108,358)(109,363)(110,364)(111,361)
(112,362)(113,367)(114,368)(115,365)(116,366)(117,371)(118,372)(119,369)
(120,370)(121,375)(122,376)(123,373)(124,374)(125,379)(126,380)(127,377)
(128,378)(129,383)(130,384)(131,381)(132,382)(133,387)(134,388)(135,385)
(136,386)(137,391)(138,392)(139,389)(140,390)(141,395)(142,396)(143,393)
(144,394)(145,399)(146,400)(147,397)(148,398)(149,403)(150,404)(151,401)
(152,402)(153,407)(154,408)(155,405)(156,406)(157,411)(158,412)(159,409)
(160,410)(161,415)(162,416)(163,413)(164,414)(165,419)(166,420)(167,417)
(168,418)(169,423)(170,424)(171,421)(172,422)(173,427)(174,428)(175,425)
(176,426)(177,431)(178,432)(179,429)(180,430)(181,435)(182,436)(183,433)
(184,434)(185,439)(186,440)(187,437)(188,438)(189,443)(190,444)(191,441)
(192,442)(193,447)(194,448)(195,445)(196,446)(197,451)(198,452)(199,449)
(200,450)(201,455)(202,456)(203,453)(204,454)(205,459)(206,460)(207,457)
(208,458)(209,463)(210,464)(211,461)(212,462)(213,467)(214,468)(215,465)
(216,466)(217,471)(218,472)(219,469)(220,470)(221,475)(222,476)(223,473)
(224,474)(225,479)(226,480)(227,477)(228,478)(229,483)(230,484)(231,481)
(232,482)(233,487)(234,488)(235,485)(236,486)(237,491)(238,492)(239,489)
(240,490)(241,495)(242,496)(243,493)(244,494)(245,499)(246,500)(247,497)
(248,498)(249,503)(250,504)(251,501)(252,502);
s1 := Sym(504)!(  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 13, 73)( 14, 74)
( 15, 76)( 16, 75)( 17, 81)( 18, 82)( 19, 84)( 20, 83)( 21, 77)( 22, 78)
( 23, 80)( 24, 79)( 25, 61)( 26, 62)( 27, 64)( 28, 63)( 29, 69)( 30, 70)
( 31, 72)( 32, 71)( 33, 65)( 34, 66)( 35, 68)( 36, 67)( 37, 49)( 38, 50)
( 39, 52)( 40, 51)( 41, 57)( 42, 58)( 43, 60)( 44, 59)( 45, 53)( 46, 54)
( 47, 56)( 48, 55)( 85,177)( 86,178)( 87,180)( 88,179)( 89,173)( 90,174)
( 91,176)( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)( 97,249)( 98,250)
( 99,252)(100,251)(101,245)(102,246)(103,248)(104,247)(105,241)(106,242)
(107,244)(108,243)(109,237)(110,238)(111,240)(112,239)(113,233)(114,234)
(115,236)(116,235)(117,229)(118,230)(119,232)(120,231)(121,225)(122,226)
(123,228)(124,227)(125,221)(126,222)(127,224)(128,223)(129,217)(130,218)
(131,220)(132,219)(133,213)(134,214)(135,216)(136,215)(137,209)(138,210)
(139,212)(140,211)(141,205)(142,206)(143,208)(144,207)(145,201)(146,202)
(147,204)(148,203)(149,197)(150,198)(151,200)(152,199)(153,193)(154,194)
(155,196)(156,195)(157,189)(158,190)(159,192)(160,191)(161,185)(162,186)
(163,188)(164,187)(165,181)(166,182)(167,184)(168,183)(255,256)(257,261)
(258,262)(259,264)(260,263)(265,325)(266,326)(267,328)(268,327)(269,333)
(270,334)(271,336)(272,335)(273,329)(274,330)(275,332)(276,331)(277,313)
(278,314)(279,316)(280,315)(281,321)(282,322)(283,324)(284,323)(285,317)
(286,318)(287,320)(288,319)(289,301)(290,302)(291,304)(292,303)(293,309)
(294,310)(295,312)(296,311)(297,305)(298,306)(299,308)(300,307)(337,429)
(338,430)(339,432)(340,431)(341,425)(342,426)(343,428)(344,427)(345,421)
(346,422)(347,424)(348,423)(349,501)(350,502)(351,504)(352,503)(353,497)
(354,498)(355,500)(356,499)(357,493)(358,494)(359,496)(360,495)(361,489)
(362,490)(363,492)(364,491)(365,485)(366,486)(367,488)(368,487)(369,481)
(370,482)(371,484)(372,483)(373,477)(374,478)(375,480)(376,479)(377,473)
(378,474)(379,476)(380,475)(381,469)(382,470)(383,472)(384,471)(385,465)
(386,466)(387,468)(388,467)(389,461)(390,462)(391,464)(392,463)(393,457)
(394,458)(395,460)(396,459)(397,453)(398,454)(399,456)(400,455)(401,449)
(402,450)(403,452)(404,451)(405,445)(406,446)(407,448)(408,447)(409,441)
(410,442)(411,444)(412,443)(413,437)(414,438)(415,440)(416,439)(417,433)
(418,434)(419,436)(420,435);
s2 := Sym(504)!(  1,349)(  2,352)(  3,351)(  4,350)(  5,357)(  6,360)(  7,359)
(  8,358)(  9,353)( 10,356)( 11,355)( 12,354)( 13,337)( 14,340)( 15,339)
( 16,338)( 17,345)( 18,348)( 19,347)( 20,346)( 21,341)( 22,344)( 23,343)
( 24,342)( 25,409)( 26,412)( 27,411)( 28,410)( 29,417)( 30,420)( 31,419)
( 32,418)( 33,413)( 34,416)( 35,415)( 36,414)( 37,397)( 38,400)( 39,399)
( 40,398)( 41,405)( 42,408)( 43,407)( 44,406)( 45,401)( 46,404)( 47,403)
( 48,402)( 49,385)( 50,388)( 51,387)( 52,386)( 53,393)( 54,396)( 55,395)
( 56,394)( 57,389)( 58,392)( 59,391)( 60,390)( 61,373)( 62,376)( 63,375)
( 64,374)( 65,381)( 66,384)( 67,383)( 68,382)( 69,377)( 70,380)( 71,379)
( 72,378)( 73,361)( 74,364)( 75,363)( 76,362)( 77,369)( 78,372)( 79,371)
( 80,370)( 81,365)( 82,368)( 83,367)( 84,366)( 85,265)( 86,268)( 87,267)
( 88,266)( 89,273)( 90,276)( 91,275)( 92,274)( 93,269)( 94,272)( 95,271)
( 96,270)( 97,253)( 98,256)( 99,255)(100,254)(101,261)(102,264)(103,263)
(104,262)(105,257)(106,260)(107,259)(108,258)(109,325)(110,328)(111,327)
(112,326)(113,333)(114,336)(115,335)(116,334)(117,329)(118,332)(119,331)
(120,330)(121,313)(122,316)(123,315)(124,314)(125,321)(126,324)(127,323)
(128,322)(129,317)(130,320)(131,319)(132,318)(133,301)(134,304)(135,303)
(136,302)(137,309)(138,312)(139,311)(140,310)(141,305)(142,308)(143,307)
(144,306)(145,289)(146,292)(147,291)(148,290)(149,297)(150,300)(151,299)
(152,298)(153,293)(154,296)(155,295)(156,294)(157,277)(158,280)(159,279)
(160,278)(161,285)(162,288)(163,287)(164,286)(165,281)(166,284)(167,283)
(168,282)(169,441)(170,444)(171,443)(172,442)(173,437)(174,440)(175,439)
(176,438)(177,433)(178,436)(179,435)(180,434)(181,429)(182,432)(183,431)
(184,430)(185,425)(186,428)(187,427)(188,426)(189,421)(190,424)(191,423)
(192,422)(193,501)(194,504)(195,503)(196,502)(197,497)(198,500)(199,499)
(200,498)(201,493)(202,496)(203,495)(204,494)(205,489)(206,492)(207,491)
(208,490)(209,485)(210,488)(211,487)(212,486)(213,481)(214,484)(215,483)
(216,482)(217,477)(218,480)(219,479)(220,478)(221,473)(222,476)(223,475)
(224,474)(225,469)(226,472)(227,471)(228,470)(229,465)(230,468)(231,467)
(232,466)(233,461)(234,464)(235,463)(236,462)(237,457)(238,460)(239,459)
(240,458)(241,453)(242,456)(243,455)(244,454)(245,449)(246,452)(247,451)
(248,450)(249,445)(250,448)(251,447)(252,446);
poly := sub<Sym(504)|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, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*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*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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