Polytope of Type {10,95}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,95}*1900
if this polytope has a name.
Group : SmallGroup(1900,29)
Rank : 3
Schlafli Type : {10,95}
Number of vertices, edges, etc : 10, 475, 95
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 : {2,95}*380
19-fold quotients : {10,5}*100
25-fold quotients : {2,19}*76
95-fold quotients : {2,5}*20
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 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);;
s1 := ( 1, 20)( 2, 38)( 3, 37)( 4, 36)( 5, 35)( 6, 34)( 7, 33)( 8, 32)
( 9, 31)( 10, 30)( 11, 29)( 12, 28)( 13, 27)( 14, 26)( 15, 25)( 16, 24)
( 17, 23)( 18, 22)( 19, 21)( 39, 77)( 40, 95)( 41, 94)( 42, 93)( 43, 92)
( 44, 91)( 45, 90)( 46, 89)( 47, 88)( 48, 87)( 49, 86)( 50, 85)( 51, 84)
( 52, 83)( 53, 82)( 54, 81)( 55, 80)( 56, 79)( 57, 78)( 59, 76)( 60, 75)
( 61, 74)( 62, 73)( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 96,400)
( 97,418)( 98,417)( 99,416)(100,415)(101,414)(102,413)(103,412)(104,411)
(105,410)(106,409)(107,408)(108,407)(109,406)(110,405)(111,404)(112,403)
(113,402)(114,401)(115,381)(116,399)(117,398)(118,397)(119,396)(120,395)
(121,394)(122,393)(123,392)(124,391)(125,390)(126,389)(127,388)(128,387)
(129,386)(130,385)(131,384)(132,383)(133,382)(134,457)(135,475)(136,474)
(137,473)(138,472)(139,471)(140,470)(141,469)(142,468)(143,467)(144,466)
(145,465)(146,464)(147,463)(148,462)(149,461)(150,460)(151,459)(152,458)
(153,438)(154,456)(155,455)(156,454)(157,453)(158,452)(159,451)(160,450)
(161,449)(162,448)(163,447)(164,446)(165,445)(166,444)(167,443)(168,442)
(169,441)(170,440)(171,439)(172,419)(173,437)(174,436)(175,435)(176,434)
(177,433)(178,432)(179,431)(180,430)(181,429)(182,428)(183,427)(184,426)
(185,425)(186,424)(187,423)(188,422)(189,421)(190,420)(191,305)(192,323)
(193,322)(194,321)(195,320)(196,319)(197,318)(198,317)(199,316)(200,315)
(201,314)(202,313)(203,312)(204,311)(205,310)(206,309)(207,308)(208,307)
(209,306)(210,286)(211,304)(212,303)(213,302)(214,301)(215,300)(216,299)
(217,298)(218,297)(219,296)(220,295)(221,294)(222,293)(223,292)(224,291)
(225,290)(226,289)(227,288)(228,287)(229,362)(230,380)(231,379)(232,378)
(233,377)(234,376)(235,375)(236,374)(237,373)(238,372)(239,371)(240,370)
(241,369)(242,368)(243,367)(244,366)(245,365)(246,364)(247,363)(248,343)
(249,361)(250,360)(251,359)(252,358)(253,357)(254,356)(255,355)(256,354)
(257,353)(258,352)(259,351)(260,350)(261,349)(262,348)(263,347)(264,346)
(265,345)(266,344)(267,324)(268,342)(269,341)(270,340)(271,339)(272,338)
(273,337)(274,336)(275,335)(276,334)(277,333)(278,332)(279,331)(280,330)
(281,329)(282,328)(283,327)(284,326)(285,325);;
s2 := ( 1, 97)( 2, 96)( 3,114)( 4,113)( 5,112)( 6,111)( 7,110)( 8,109)
( 9,108)( 10,107)( 11,106)( 12,105)( 13,104)( 14,103)( 15,102)( 16,101)
( 17,100)( 18, 99)( 19, 98)( 20,173)( 21,172)( 22,190)( 23,189)( 24,188)
( 25,187)( 26,186)( 27,185)( 28,184)( 29,183)( 30,182)( 31,181)( 32,180)
( 33,179)( 34,178)( 35,177)( 36,176)( 37,175)( 38,174)( 39,154)( 40,153)
( 41,171)( 42,170)( 43,169)( 44,168)( 45,167)( 46,166)( 47,165)( 48,164)
( 49,163)( 50,162)( 51,161)( 52,160)( 53,159)( 54,158)( 55,157)( 56,156)
( 57,155)( 58,135)( 59,134)( 60,152)( 61,151)( 62,150)( 63,149)( 64,148)
( 65,147)( 66,146)( 67,145)( 68,144)( 69,143)( 70,142)( 71,141)( 72,140)
( 73,139)( 74,138)( 75,137)( 76,136)( 77,116)( 78,115)( 79,133)( 80,132)
( 81,131)( 82,130)( 83,129)( 84,128)( 85,127)( 86,126)( 87,125)( 88,124)
( 89,123)( 90,122)( 91,121)( 92,120)( 93,119)( 94,118)( 95,117)(191,382)
(192,381)(193,399)(194,398)(195,397)(196,396)(197,395)(198,394)(199,393)
(200,392)(201,391)(202,390)(203,389)(204,388)(205,387)(206,386)(207,385)
(208,384)(209,383)(210,458)(211,457)(212,475)(213,474)(214,473)(215,472)
(216,471)(217,470)(218,469)(219,468)(220,467)(221,466)(222,465)(223,464)
(224,463)(225,462)(226,461)(227,460)(228,459)(229,439)(230,438)(231,456)
(232,455)(233,454)(234,453)(235,452)(236,451)(237,450)(238,449)(239,448)
(240,447)(241,446)(242,445)(243,444)(244,443)(245,442)(246,441)(247,440)
(248,420)(249,419)(250,437)(251,436)(252,435)(253,434)(254,433)(255,432)
(256,431)(257,430)(258,429)(259,428)(260,427)(261,426)(262,425)(263,424)
(264,423)(265,422)(266,421)(267,401)(268,400)(269,418)(270,417)(271,416)
(272,415)(273,414)(274,413)(275,412)(276,411)(277,410)(278,409)(279,408)
(280,407)(281,406)(282,405)(283,404)(284,403)(285,402)(286,287)(288,304)
(289,303)(290,302)(291,301)(292,300)(293,299)(294,298)(295,297)(305,363)
(306,362)(307,380)(308,379)(309,378)(310,377)(311,376)(312,375)(313,374)
(314,373)(315,372)(316,371)(317,370)(318,369)(319,368)(320,367)(321,366)
(322,365)(323,364)(324,344)(325,343)(326,361)(327,360)(328,359)(329,358)
(330,357)(331,356)(332,355)(333,354)(334,353)(335,352)(336,351)(337,350)
(338,349)(339,348)(340,347)(341,346)(342,345);;
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*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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);
s1 := Sym(475)!( 1, 20)( 2, 38)( 3, 37)( 4, 36)( 5, 35)( 6, 34)( 7, 33)
( 8, 32)( 9, 31)( 10, 30)( 11, 29)( 12, 28)( 13, 27)( 14, 26)( 15, 25)
( 16, 24)( 17, 23)( 18, 22)( 19, 21)( 39, 77)( 40, 95)( 41, 94)( 42, 93)
( 43, 92)( 44, 91)( 45, 90)( 46, 89)( 47, 88)( 48, 87)( 49, 86)( 50, 85)
( 51, 84)( 52, 83)( 53, 82)( 54, 81)( 55, 80)( 56, 79)( 57, 78)( 59, 76)
( 60, 75)( 61, 74)( 62, 73)( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 67, 68)
( 96,400)( 97,418)( 98,417)( 99,416)(100,415)(101,414)(102,413)(103,412)
(104,411)(105,410)(106,409)(107,408)(108,407)(109,406)(110,405)(111,404)
(112,403)(113,402)(114,401)(115,381)(116,399)(117,398)(118,397)(119,396)
(120,395)(121,394)(122,393)(123,392)(124,391)(125,390)(126,389)(127,388)
(128,387)(129,386)(130,385)(131,384)(132,383)(133,382)(134,457)(135,475)
(136,474)(137,473)(138,472)(139,471)(140,470)(141,469)(142,468)(143,467)
(144,466)(145,465)(146,464)(147,463)(148,462)(149,461)(150,460)(151,459)
(152,458)(153,438)(154,456)(155,455)(156,454)(157,453)(158,452)(159,451)
(160,450)(161,449)(162,448)(163,447)(164,446)(165,445)(166,444)(167,443)
(168,442)(169,441)(170,440)(171,439)(172,419)(173,437)(174,436)(175,435)
(176,434)(177,433)(178,432)(179,431)(180,430)(181,429)(182,428)(183,427)
(184,426)(185,425)(186,424)(187,423)(188,422)(189,421)(190,420)(191,305)
(192,323)(193,322)(194,321)(195,320)(196,319)(197,318)(198,317)(199,316)
(200,315)(201,314)(202,313)(203,312)(204,311)(205,310)(206,309)(207,308)
(208,307)(209,306)(210,286)(211,304)(212,303)(213,302)(214,301)(215,300)
(216,299)(217,298)(218,297)(219,296)(220,295)(221,294)(222,293)(223,292)
(224,291)(225,290)(226,289)(227,288)(228,287)(229,362)(230,380)(231,379)
(232,378)(233,377)(234,376)(235,375)(236,374)(237,373)(238,372)(239,371)
(240,370)(241,369)(242,368)(243,367)(244,366)(245,365)(246,364)(247,363)
(248,343)(249,361)(250,360)(251,359)(252,358)(253,357)(254,356)(255,355)
(256,354)(257,353)(258,352)(259,351)(260,350)(261,349)(262,348)(263,347)
(264,346)(265,345)(266,344)(267,324)(268,342)(269,341)(270,340)(271,339)
(272,338)(273,337)(274,336)(275,335)(276,334)(277,333)(278,332)(279,331)
(280,330)(281,329)(282,328)(283,327)(284,326)(285,325);
s2 := Sym(475)!( 1, 97)( 2, 96)( 3,114)( 4,113)( 5,112)( 6,111)( 7,110)
( 8,109)( 9,108)( 10,107)( 11,106)( 12,105)( 13,104)( 14,103)( 15,102)
( 16,101)( 17,100)( 18, 99)( 19, 98)( 20,173)( 21,172)( 22,190)( 23,189)
( 24,188)( 25,187)( 26,186)( 27,185)( 28,184)( 29,183)( 30,182)( 31,181)
( 32,180)( 33,179)( 34,178)( 35,177)( 36,176)( 37,175)( 38,174)( 39,154)
( 40,153)( 41,171)( 42,170)( 43,169)( 44,168)( 45,167)( 46,166)( 47,165)
( 48,164)( 49,163)( 50,162)( 51,161)( 52,160)( 53,159)( 54,158)( 55,157)
( 56,156)( 57,155)( 58,135)( 59,134)( 60,152)( 61,151)( 62,150)( 63,149)
( 64,148)( 65,147)( 66,146)( 67,145)( 68,144)( 69,143)( 70,142)( 71,141)
( 72,140)( 73,139)( 74,138)( 75,137)( 76,136)( 77,116)( 78,115)( 79,133)
( 80,132)( 81,131)( 82,130)( 83,129)( 84,128)( 85,127)( 86,126)( 87,125)
( 88,124)( 89,123)( 90,122)( 91,121)( 92,120)( 93,119)( 94,118)( 95,117)
(191,382)(192,381)(193,399)(194,398)(195,397)(196,396)(197,395)(198,394)
(199,393)(200,392)(201,391)(202,390)(203,389)(204,388)(205,387)(206,386)
(207,385)(208,384)(209,383)(210,458)(211,457)(212,475)(213,474)(214,473)
(215,472)(216,471)(217,470)(218,469)(219,468)(220,467)(221,466)(222,465)
(223,464)(224,463)(225,462)(226,461)(227,460)(228,459)(229,439)(230,438)
(231,456)(232,455)(233,454)(234,453)(235,452)(236,451)(237,450)(238,449)
(239,448)(240,447)(241,446)(242,445)(243,444)(244,443)(245,442)(246,441)
(247,440)(248,420)(249,419)(250,437)(251,436)(252,435)(253,434)(254,433)
(255,432)(256,431)(257,430)(258,429)(259,428)(260,427)(261,426)(262,425)
(263,424)(264,423)(265,422)(266,421)(267,401)(268,400)(269,418)(270,417)
(271,416)(272,415)(273,414)(274,413)(275,412)(276,411)(277,410)(278,409)
(279,408)(280,407)(281,406)(282,405)(283,404)(284,403)(285,402)(286,287)
(288,304)(289,303)(290,302)(291,301)(292,300)(293,299)(294,298)(295,297)
(305,363)(306,362)(307,380)(308,379)(309,378)(310,377)(311,376)(312,375)
(313,374)(314,373)(315,372)(316,371)(317,370)(318,369)(319,368)(320,367)
(321,366)(322,365)(323,364)(324,344)(325,343)(326,361)(327,360)(328,359)
(329,358)(330,357)(331,356)(332,355)(333,354)(334,353)(335,352)(336,351)
(337,350)(338,349)(339,348)(340,347)(341,346)(342,345);
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*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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 >;
References : None.
to this polytope