Polytope of Type {95,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {95,10}*1900
if this polytope has a name.
Group : SmallGroup(1900,29)
Rank : 3
Schlafli Type : {95,10}
Number of vertices, edges, etc : 95, 475, 10
Order of s₀s₁s₂ : 190
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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) :
   5-fold quotients : {95,2}*380
   19-fold quotients : {5,10}*100
   25-fold quotients : {19,2}*76
   95-fold quotients : {5,2}*20
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)(  9, 12)
( 10, 11)( 20, 77)( 21, 95)( 22, 94)( 23, 93)( 24, 92)( 25, 91)( 26, 90)
( 27, 89)( 28, 88)( 29, 87)( 30, 86)( 31, 85)( 32, 84)( 33, 83)( 34, 82)
( 35, 81)( 36, 80)( 37, 79)( 38, 78)( 39, 58)( 40, 76)( 41, 75)( 42, 74)
( 43, 73)( 44, 72)( 45, 71)( 46, 70)( 47, 69)( 48, 68)( 49, 67)( 50, 66)
( 51, 65)( 52, 64)( 53, 63)( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 96,381)
( 97,399)( 98,398)( 99,397)(100,396)(101,395)(102,394)(103,393)(104,392)
(105,391)(106,390)(107,389)(108,388)(109,387)(110,386)(111,385)(112,384)
(113,383)(114,382)(115,457)(116,475)(117,474)(118,473)(119,472)(120,471)
(121,470)(122,469)(123,468)(124,467)(125,466)(126,465)(127,464)(128,463)
(129,462)(130,461)(131,460)(132,459)(133,458)(134,438)(135,456)(136,455)
(137,454)(138,453)(139,452)(140,451)(141,450)(142,449)(143,448)(144,447)
(145,446)(146,445)(147,444)(148,443)(149,442)(150,441)(151,440)(152,439)
(153,419)(154,437)(155,436)(156,435)(157,434)(158,433)(159,432)(160,431)
(161,430)(162,429)(163,428)(164,427)(165,426)(166,425)(167,424)(168,423)
(169,422)(170,421)(171,420)(172,400)(173,418)(174,417)(175,416)(176,415)
(177,414)(178,413)(179,412)(180,411)(181,410)(182,409)(183,408)(184,407)
(185,406)(186,405)(187,404)(188,403)(189,402)(190,401)(191,286)(192,304)
(193,303)(194,302)(195,301)(196,300)(197,299)(198,298)(199,297)(200,296)
(201,295)(202,294)(203,293)(204,292)(205,291)(206,290)(207,289)(208,288)
(209,287)(210,362)(211,380)(212,379)(213,378)(214,377)(215,376)(216,375)
(217,374)(218,373)(219,372)(220,371)(221,370)(222,369)(223,368)(224,367)
(225,366)(226,365)(227,364)(228,363)(229,343)(230,361)(231,360)(232,359)
(233,358)(234,357)(235,356)(236,355)(237,354)(238,353)(239,352)(240,351)
(241,350)(242,349)(243,348)(244,347)(245,346)(246,345)(247,344)(248,324)
(249,342)(250,341)(251,340)(252,339)(253,338)(254,337)(255,336)(256,335)
(257,334)(258,333)(259,332)(260,331)(261,330)(262,329)(263,328)(264,327)
(265,326)(266,325)(267,305)(268,323)(269,322)(270,321)(271,320)(272,319)
(273,318)(274,317)(275,316)(276,315)(277,314)(278,313)(279,312)(280,311)
(281,310)(282,309)(283,308)(284,307)(285,306);;
s1 := (  1,116)(  2,115)(  3,133)(  4,132)(  5,131)(  6,130)(  7,129)(  8,128)
(  9,127)( 10,126)( 11,125)( 12,124)( 13,123)( 14,122)( 15,121)( 16,120)
( 17,119)( 18,118)( 19,117)( 20, 97)( 21, 96)( 22,114)( 23,113)( 24,112)
( 25,111)( 26,110)( 27,109)( 28,108)( 29,107)( 30,106)( 31,105)( 32,104)
( 33,103)( 34,102)( 35,101)( 36,100)( 37, 99)( 38, 98)( 39,173)( 40,172)
( 41,190)( 42,189)( 43,188)( 44,187)( 45,186)( 46,185)( 47,184)( 48,183)
( 49,182)( 50,181)( 51,180)( 52,179)( 53,178)( 54,177)( 55,176)( 56,175)
( 57,174)( 58,154)( 59,153)( 60,171)( 61,170)( 62,169)( 63,168)( 64,167)
( 65,166)( 66,165)( 67,164)( 68,163)( 69,162)( 70,161)( 71,160)( 72,159)
( 73,158)( 74,157)( 75,156)( 76,155)( 77,135)( 78,134)( 79,152)( 80,151)
( 81,150)( 82,149)( 83,148)( 84,147)( 85,146)( 86,145)( 87,144)( 88,143)
( 89,142)( 90,141)( 91,140)( 92,139)( 93,138)( 94,137)( 95,136)(191,401)
(192,400)(193,418)(194,417)(195,416)(196,415)(197,414)(198,413)(199,412)
(200,411)(201,410)(202,409)(203,408)(204,407)(205,406)(206,405)(207,404)
(208,403)(209,402)(210,382)(211,381)(212,399)(213,398)(214,397)(215,396)
(216,395)(217,394)(218,393)(219,392)(220,391)(221,390)(222,389)(223,388)
(224,387)(225,386)(226,385)(227,384)(228,383)(229,458)(230,457)(231,475)
(232,474)(233,473)(234,472)(235,471)(236,470)(237,469)(238,468)(239,467)
(240,466)(241,465)(242,464)(243,463)(244,462)(245,461)(246,460)(247,459)
(248,439)(249,438)(250,456)(251,455)(252,454)(253,453)(254,452)(255,451)
(256,450)(257,449)(258,448)(259,447)(260,446)(261,445)(262,444)(263,443)
(264,442)(265,441)(266,440)(267,420)(268,419)(269,437)(270,436)(271,435)
(272,434)(273,433)(274,432)(275,431)(276,430)(277,429)(278,428)(279,427)
(280,426)(281,425)(282,424)(283,423)(284,422)(285,421)(286,306)(287,305)
(288,323)(289,322)(290,321)(291,320)(292,319)(293,318)(294,317)(295,316)
(296,315)(297,314)(298,313)(299,312)(300,311)(301,310)(302,309)(303,308)
(304,307)(324,363)(325,362)(326,380)(327,379)(328,378)(329,377)(330,376)
(331,375)(332,374)(333,373)(334,372)(335,371)(336,370)(337,369)(338,368)
(339,367)(340,366)(341,365)(342,364)(343,344)(345,361)(346,360)(347,359)
(348,358)(349,357)(350,356)(351,355)(352,354);;
s2 := ( 20, 77)( 21, 78)( 22, 79)( 23, 80)( 24, 81)( 25, 82)( 26, 83)( 27, 84)
( 28, 85)( 29, 86)( 30, 87)( 31, 88)( 32, 89)( 33, 90)( 34, 91)( 35, 92)
( 36, 93)( 37, 94)( 38, 95)( 39, 58)( 40, 59)( 41, 60)( 42, 61)( 43, 62)
( 44, 63)( 45, 64)( 46, 65)( 47, 66)( 48, 67)( 49, 68)( 50, 69)( 51, 70)
( 52, 71)( 53, 72)( 54, 73)( 55, 74)( 56, 75)( 57, 76)(115,172)(116,173)
(117,174)(118,175)(119,176)(120,177)(121,178)(122,179)(123,180)(124,181)
(125,182)(126,183)(127,184)(128,185)(129,186)(130,187)(131,188)(132,189)
(133,190)(134,153)(135,154)(136,155)(137,156)(138,157)(139,158)(140,159)
(141,160)(142,161)(143,162)(144,163)(145,164)(146,165)(147,166)(148,167)
(149,168)(150,169)(151,170)(152,171)(210,267)(211,268)(212,269)(213,270)
(214,271)(215,272)(216,273)(217,274)(218,275)(219,276)(220,277)(221,278)
(222,279)(223,280)(224,281)(225,282)(226,283)(227,284)(228,285)(229,248)
(230,249)(231,250)(232,251)(233,252)(234,253)(235,254)(236,255)(237,256)
(238,257)(239,258)(240,259)(241,260)(242,261)(243,262)(244,263)(245,264)
(246,265)(247,266)(305,362)(306,363)(307,364)(308,365)(309,366)(310,367)
(311,368)(312,369)(313,370)(314,371)(315,372)(316,373)(317,374)(318,375)
(319,376)(320,377)(321,378)(322,379)(323,380)(324,343)(325,344)(326,345)
(327,346)(328,347)(329,348)(330,349)(331,350)(332,351)(333,352)(334,353)
(335,354)(336,355)(337,356)(338,357)(339,358)(340,359)(341,360)(342,361)
(400,457)(401,458)(402,459)(403,460)(404,461)(405,462)(406,463)(407,464)
(408,465)(409,466)(410,467)(411,468)(412,469)(413,470)(414,471)(415,472)
(416,473)(417,474)(418,475)(419,438)(420,439)(421,440)(422,441)(423,442)
(424,443)(425,444)(426,445)(427,446)(428,447)(429,448)(430,449)(431,450)
(432,451)(433,452)(434,453)(435,454)(436,455)(437,456);;
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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(475)!(  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)
(  9, 12)( 10, 11)( 20, 77)( 21, 95)( 22, 94)( 23, 93)( 24, 92)( 25, 91)
( 26, 90)( 27, 89)( 28, 88)( 29, 87)( 30, 86)( 31, 85)( 32, 84)( 33, 83)
( 34, 82)( 35, 81)( 36, 80)( 37, 79)( 38, 78)( 39, 58)( 40, 76)( 41, 75)
( 42, 74)( 43, 73)( 44, 72)( 45, 71)( 46, 70)( 47, 69)( 48, 68)( 49, 67)
( 50, 66)( 51, 65)( 52, 64)( 53, 63)( 54, 62)( 55, 61)( 56, 60)( 57, 59)
( 96,381)( 97,399)( 98,398)( 99,397)(100,396)(101,395)(102,394)(103,393)
(104,392)(105,391)(106,390)(107,389)(108,388)(109,387)(110,386)(111,385)
(112,384)(113,383)(114,382)(115,457)(116,475)(117,474)(118,473)(119,472)
(120,471)(121,470)(122,469)(123,468)(124,467)(125,466)(126,465)(127,464)
(128,463)(129,462)(130,461)(131,460)(132,459)(133,458)(134,438)(135,456)
(136,455)(137,454)(138,453)(139,452)(140,451)(141,450)(142,449)(143,448)
(144,447)(145,446)(146,445)(147,444)(148,443)(149,442)(150,441)(151,440)
(152,439)(153,419)(154,437)(155,436)(156,435)(157,434)(158,433)(159,432)
(160,431)(161,430)(162,429)(163,428)(164,427)(165,426)(166,425)(167,424)
(168,423)(169,422)(170,421)(171,420)(172,400)(173,418)(174,417)(175,416)
(176,415)(177,414)(178,413)(179,412)(180,411)(181,410)(182,409)(183,408)
(184,407)(185,406)(186,405)(187,404)(188,403)(189,402)(190,401)(191,286)
(192,304)(193,303)(194,302)(195,301)(196,300)(197,299)(198,298)(199,297)
(200,296)(201,295)(202,294)(203,293)(204,292)(205,291)(206,290)(207,289)
(208,288)(209,287)(210,362)(211,380)(212,379)(213,378)(214,377)(215,376)
(216,375)(217,374)(218,373)(219,372)(220,371)(221,370)(222,369)(223,368)
(224,367)(225,366)(226,365)(227,364)(228,363)(229,343)(230,361)(231,360)
(232,359)(233,358)(234,357)(235,356)(236,355)(237,354)(238,353)(239,352)
(240,351)(241,350)(242,349)(243,348)(244,347)(245,346)(246,345)(247,344)
(248,324)(249,342)(250,341)(251,340)(252,339)(253,338)(254,337)(255,336)
(256,335)(257,334)(258,333)(259,332)(260,331)(261,330)(262,329)(263,328)
(264,327)(265,326)(266,325)(267,305)(268,323)(269,322)(270,321)(271,320)
(272,319)(273,318)(274,317)(275,316)(276,315)(277,314)(278,313)(279,312)
(280,311)(281,310)(282,309)(283,308)(284,307)(285,306);
s1 := Sym(475)!(  1,116)(  2,115)(  3,133)(  4,132)(  5,131)(  6,130)(  7,129)
(  8,128)(  9,127)( 10,126)( 11,125)( 12,124)( 13,123)( 14,122)( 15,121)
( 16,120)( 17,119)( 18,118)( 19,117)( 20, 97)( 21, 96)( 22,114)( 23,113)
( 24,112)( 25,111)( 26,110)( 27,109)( 28,108)( 29,107)( 30,106)( 31,105)
( 32,104)( 33,103)( 34,102)( 35,101)( 36,100)( 37, 99)( 38, 98)( 39,173)
( 40,172)( 41,190)( 42,189)( 43,188)( 44,187)( 45,186)( 46,185)( 47,184)
( 48,183)( 49,182)( 50,181)( 51,180)( 52,179)( 53,178)( 54,177)( 55,176)
( 56,175)( 57,174)( 58,154)( 59,153)( 60,171)( 61,170)( 62,169)( 63,168)
( 64,167)( 65,166)( 66,165)( 67,164)( 68,163)( 69,162)( 70,161)( 71,160)
( 72,159)( 73,158)( 74,157)( 75,156)( 76,155)( 77,135)( 78,134)( 79,152)
( 80,151)( 81,150)( 82,149)( 83,148)( 84,147)( 85,146)( 86,145)( 87,144)
( 88,143)( 89,142)( 90,141)( 91,140)( 92,139)( 93,138)( 94,137)( 95,136)
(191,401)(192,400)(193,418)(194,417)(195,416)(196,415)(197,414)(198,413)
(199,412)(200,411)(201,410)(202,409)(203,408)(204,407)(205,406)(206,405)
(207,404)(208,403)(209,402)(210,382)(211,381)(212,399)(213,398)(214,397)
(215,396)(216,395)(217,394)(218,393)(219,392)(220,391)(221,390)(222,389)
(223,388)(224,387)(225,386)(226,385)(227,384)(228,383)(229,458)(230,457)
(231,475)(232,474)(233,473)(234,472)(235,471)(236,470)(237,469)(238,468)
(239,467)(240,466)(241,465)(242,464)(243,463)(244,462)(245,461)(246,460)
(247,459)(248,439)(249,438)(250,456)(251,455)(252,454)(253,453)(254,452)
(255,451)(256,450)(257,449)(258,448)(259,447)(260,446)(261,445)(262,444)
(263,443)(264,442)(265,441)(266,440)(267,420)(268,419)(269,437)(270,436)
(271,435)(272,434)(273,433)(274,432)(275,431)(276,430)(277,429)(278,428)
(279,427)(280,426)(281,425)(282,424)(283,423)(284,422)(285,421)(286,306)
(287,305)(288,323)(289,322)(290,321)(291,320)(292,319)(293,318)(294,317)
(295,316)(296,315)(297,314)(298,313)(299,312)(300,311)(301,310)(302,309)
(303,308)(304,307)(324,363)(325,362)(326,380)(327,379)(328,378)(329,377)
(330,376)(331,375)(332,374)(333,373)(334,372)(335,371)(336,370)(337,369)
(338,368)(339,367)(340,366)(341,365)(342,364)(343,344)(345,361)(346,360)
(347,359)(348,358)(349,357)(350,356)(351,355)(352,354);
s2 := Sym(475)!( 20, 77)( 21, 78)( 22, 79)( 23, 80)( 24, 81)( 25, 82)( 26, 83)
( 27, 84)( 28, 85)( 29, 86)( 30, 87)( 31, 88)( 32, 89)( 33, 90)( 34, 91)
( 35, 92)( 36, 93)( 37, 94)( 38, 95)( 39, 58)( 40, 59)( 41, 60)( 42, 61)
( 43, 62)( 44, 63)( 45, 64)( 46, 65)( 47, 66)( 48, 67)( 49, 68)( 50, 69)
( 51, 70)( 52, 71)( 53, 72)( 54, 73)( 55, 74)( 56, 75)( 57, 76)(115,172)
(116,173)(117,174)(118,175)(119,176)(120,177)(121,178)(122,179)(123,180)
(124,181)(125,182)(126,183)(127,184)(128,185)(129,186)(130,187)(131,188)
(132,189)(133,190)(134,153)(135,154)(136,155)(137,156)(138,157)(139,158)
(140,159)(141,160)(142,161)(143,162)(144,163)(145,164)(146,165)(147,166)
(148,167)(149,168)(150,169)(151,170)(152,171)(210,267)(211,268)(212,269)
(213,270)(214,271)(215,272)(216,273)(217,274)(218,275)(219,276)(220,277)
(221,278)(222,279)(223,280)(224,281)(225,282)(226,283)(227,284)(228,285)
(229,248)(230,249)(231,250)(232,251)(233,252)(234,253)(235,254)(236,255)
(237,256)(238,257)(239,258)(240,259)(241,260)(242,261)(243,262)(244,263)
(245,264)(246,265)(247,266)(305,362)(306,363)(307,364)(308,365)(309,366)
(310,367)(311,368)(312,369)(313,370)(314,371)(315,372)(316,373)(317,374)
(318,375)(319,376)(320,377)(321,378)(322,379)(323,380)(324,343)(325,344)
(326,345)(327,346)(328,347)(329,348)(330,349)(331,350)(332,351)(333,352)
(334,353)(335,354)(336,355)(337,356)(338,357)(339,358)(340,359)(341,360)
(342,361)(400,457)(401,458)(402,459)(403,460)(404,461)(405,462)(406,463)
(407,464)(408,465)(409,466)(410,467)(411,468)(412,469)(413,470)(414,471)
(415,472)(416,473)(417,474)(418,475)(419,438)(420,439)(421,440)(422,441)
(423,442)(424,443)(425,444)(426,445)(427,446)(428,447)(429,448)(430,449)
(431,450)(432,451)(433,452)(434,453)(435,454)(436,455)(437,456);
poly := sub<Sym(475)|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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope