Polytope of Type {94,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {94,10}*1880
Also Known As : {94,10|2}. if this polytope has another name.
Group : SmallGroup(1880,35)
Rank : 3
Schlafli Type : {94,10}
Number of vertices, edges, etc : 94, 470, 10
Order of s0s1s2 : 470
Order of s0s1s2s1 : 2
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 : {94,2}*376
10-fold quotients : {47,2}*188
47-fold quotients : {2,10}*40
94-fold quotients : {2,5}*20
235-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 47)( 3, 46)( 4, 45)( 5, 44)( 6, 43)( 7, 42)( 8, 41)( 9, 40)
( 10, 39)( 11, 38)( 12, 37)( 13, 36)( 14, 35)( 15, 34)( 16, 33)( 17, 32)
( 18, 31)( 19, 30)( 20, 29)( 21, 28)( 22, 27)( 23, 26)( 24, 25)( 49, 94)
( 50, 93)( 51, 92)( 52, 91)( 53, 90)( 54, 89)( 55, 88)( 56, 87)( 57, 86)
( 58, 85)( 59, 84)( 60, 83)( 61, 82)( 62, 81)( 63, 80)( 64, 79)( 65, 78)
( 66, 77)( 67, 76)( 68, 75)( 69, 74)( 70, 73)( 71, 72)( 96,141)( 97,140)
( 98,139)( 99,138)(100,137)(101,136)(102,135)(103,134)(104,133)(105,132)
(106,131)(107,130)(108,129)(109,128)(110,127)(111,126)(112,125)(113,124)
(114,123)(115,122)(116,121)(117,120)(118,119)(143,188)(144,187)(145,186)
(146,185)(147,184)(148,183)(149,182)(150,181)(151,180)(152,179)(153,178)
(154,177)(155,176)(156,175)(157,174)(158,173)(159,172)(160,171)(161,170)
(162,169)(163,168)(164,167)(165,166)(190,235)(191,234)(192,233)(193,232)
(194,231)(195,230)(196,229)(197,228)(198,227)(199,226)(200,225)(201,224)
(202,223)(203,222)(204,221)(205,220)(206,219)(207,218)(208,217)(209,216)
(210,215)(211,214)(212,213)(237,282)(238,281)(239,280)(240,279)(241,278)
(242,277)(243,276)(244,275)(245,274)(246,273)(247,272)(248,271)(249,270)
(250,269)(251,268)(252,267)(253,266)(254,265)(255,264)(256,263)(257,262)
(258,261)(259,260)(284,329)(285,328)(286,327)(287,326)(288,325)(289,324)
(290,323)(291,322)(292,321)(293,320)(294,319)(295,318)(296,317)(297,316)
(298,315)(299,314)(300,313)(301,312)(302,311)(303,310)(304,309)(305,308)
(306,307)(331,376)(332,375)(333,374)(334,373)(335,372)(336,371)(337,370)
(338,369)(339,368)(340,367)(341,366)(342,365)(343,364)(344,363)(345,362)
(346,361)(347,360)(348,359)(349,358)(350,357)(351,356)(352,355)(353,354)
(378,423)(379,422)(380,421)(381,420)(382,419)(383,418)(384,417)(385,416)
(386,415)(387,414)(388,413)(389,412)(390,411)(391,410)(392,409)(393,408)
(394,407)(395,406)(396,405)(397,404)(398,403)(399,402)(400,401)(425,470)
(426,469)(427,468)(428,467)(429,466)(430,465)(431,464)(432,463)(433,462)
(434,461)(435,460)(436,459)(437,458)(438,457)(439,456)(440,455)(441,454)
(442,453)(443,452)(444,451)(445,450)(446,449)(447,448);;
s1 := ( 1, 2)( 3, 47)( 4, 46)( 5, 45)( 6, 44)( 7, 43)( 8, 42)( 9, 41)
( 10, 40)( 11, 39)( 12, 38)( 13, 37)( 14, 36)( 15, 35)( 16, 34)( 17, 33)
( 18, 32)( 19, 31)( 20, 30)( 21, 29)( 22, 28)( 23, 27)( 24, 26)( 48,190)
( 49,189)( 50,235)( 51,234)( 52,233)( 53,232)( 54,231)( 55,230)( 56,229)
( 57,228)( 58,227)( 59,226)( 60,225)( 61,224)( 62,223)( 63,222)( 64,221)
( 65,220)( 66,219)( 67,218)( 68,217)( 69,216)( 70,215)( 71,214)( 72,213)
( 73,212)( 74,211)( 75,210)( 76,209)( 77,208)( 78,207)( 79,206)( 80,205)
( 81,204)( 82,203)( 83,202)( 84,201)( 85,200)( 86,199)( 87,198)( 88,197)
( 89,196)( 90,195)( 91,194)( 92,193)( 93,192)( 94,191)( 95,143)( 96,142)
( 97,188)( 98,187)( 99,186)(100,185)(101,184)(102,183)(103,182)(104,181)
(105,180)(106,179)(107,178)(108,177)(109,176)(110,175)(111,174)(112,173)
(113,172)(114,171)(115,170)(116,169)(117,168)(118,167)(119,166)(120,165)
(121,164)(122,163)(123,162)(124,161)(125,160)(126,159)(127,158)(128,157)
(129,156)(130,155)(131,154)(132,153)(133,152)(134,151)(135,150)(136,149)
(137,148)(138,147)(139,146)(140,145)(141,144)(236,237)(238,282)(239,281)
(240,280)(241,279)(242,278)(243,277)(244,276)(245,275)(246,274)(247,273)
(248,272)(249,271)(250,270)(251,269)(252,268)(253,267)(254,266)(255,265)
(256,264)(257,263)(258,262)(259,261)(283,425)(284,424)(285,470)(286,469)
(287,468)(288,467)(289,466)(290,465)(291,464)(292,463)(293,462)(294,461)
(295,460)(296,459)(297,458)(298,457)(299,456)(300,455)(301,454)(302,453)
(303,452)(304,451)(305,450)(306,449)(307,448)(308,447)(309,446)(310,445)
(311,444)(312,443)(313,442)(314,441)(315,440)(316,439)(317,438)(318,437)
(319,436)(320,435)(321,434)(322,433)(323,432)(324,431)(325,430)(326,429)
(327,428)(328,427)(329,426)(330,378)(331,377)(332,423)(333,422)(334,421)
(335,420)(336,419)(337,418)(338,417)(339,416)(340,415)(341,414)(342,413)
(343,412)(344,411)(345,410)(346,409)(347,408)(348,407)(349,406)(350,405)
(351,404)(352,403)(353,402)(354,401)(355,400)(356,399)(357,398)(358,397)
(359,396)(360,395)(361,394)(362,393)(363,392)(364,391)(365,390)(366,389)
(367,388)(368,387)(369,386)(370,385)(371,384)(372,383)(373,382)(374,381)
(375,380)(376,379);;
s2 := ( 1,283)( 2,284)( 3,285)( 4,286)( 5,287)( 6,288)( 7,289)( 8,290)
( 9,291)( 10,292)( 11,293)( 12,294)( 13,295)( 14,296)( 15,297)( 16,298)
( 17,299)( 18,300)( 19,301)( 20,302)( 21,303)( 22,304)( 23,305)( 24,306)
( 25,307)( 26,308)( 27,309)( 28,310)( 29,311)( 30,312)( 31,313)( 32,314)
( 33,315)( 34,316)( 35,317)( 36,318)( 37,319)( 38,320)( 39,321)( 40,322)
( 41,323)( 42,324)( 43,325)( 44,326)( 45,327)( 46,328)( 47,329)( 48,236)
( 49,237)( 50,238)( 51,239)( 52,240)( 53,241)( 54,242)( 55,243)( 56,244)
( 57,245)( 58,246)( 59,247)( 60,248)( 61,249)( 62,250)( 63,251)( 64,252)
( 65,253)( 66,254)( 67,255)( 68,256)( 69,257)( 70,258)( 71,259)( 72,260)
( 73,261)( 74,262)( 75,263)( 76,264)( 77,265)( 78,266)( 79,267)( 80,268)
( 81,269)( 82,270)( 83,271)( 84,272)( 85,273)( 86,274)( 87,275)( 88,276)
( 89,277)( 90,278)( 91,279)( 92,280)( 93,281)( 94,282)( 95,424)( 96,425)
( 97,426)( 98,427)( 99,428)(100,429)(101,430)(102,431)(103,432)(104,433)
(105,434)(106,435)(107,436)(108,437)(109,438)(110,439)(111,440)(112,441)
(113,442)(114,443)(115,444)(116,445)(117,446)(118,447)(119,448)(120,449)
(121,450)(122,451)(123,452)(124,453)(125,454)(126,455)(127,456)(128,457)
(129,458)(130,459)(131,460)(132,461)(133,462)(134,463)(135,464)(136,465)
(137,466)(138,467)(139,468)(140,469)(141,470)(142,377)(143,378)(144,379)
(145,380)(146,381)(147,382)(148,383)(149,384)(150,385)(151,386)(152,387)
(153,388)(154,389)(155,390)(156,391)(157,392)(158,393)(159,394)(160,395)
(161,396)(162,397)(163,398)(164,399)(165,400)(166,401)(167,402)(168,403)
(169,404)(170,405)(171,406)(172,407)(173,408)(174,409)(175,410)(176,411)
(177,412)(178,413)(179,414)(180,415)(181,416)(182,417)(183,418)(184,419)
(185,420)(186,421)(187,422)(188,423)(189,330)(190,331)(191,332)(192,333)
(193,334)(194,335)(195,336)(196,337)(197,338)(198,339)(199,340)(200,341)
(201,342)(202,343)(203,344)(204,345)(205,346)(206,347)(207,348)(208,349)
(209,350)(210,351)(211,352)(212,353)(213,354)(214,355)(215,356)(216,357)
(217,358)(218,359)(219,360)(220,361)(221,362)(222,363)(223,364)(224,365)
(225,366)(226,367)(227,368)(228,369)(229,370)(230,371)(231,372)(232,373)
(233,374)(234,375)(235,376);;
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*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*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(470)!( 2, 47)( 3, 46)( 4, 45)( 5, 44)( 6, 43)( 7, 42)( 8, 41)
( 9, 40)( 10, 39)( 11, 38)( 12, 37)( 13, 36)( 14, 35)( 15, 34)( 16, 33)
( 17, 32)( 18, 31)( 19, 30)( 20, 29)( 21, 28)( 22, 27)( 23, 26)( 24, 25)
( 49, 94)( 50, 93)( 51, 92)( 52, 91)( 53, 90)( 54, 89)( 55, 88)( 56, 87)
( 57, 86)( 58, 85)( 59, 84)( 60, 83)( 61, 82)( 62, 81)( 63, 80)( 64, 79)
( 65, 78)( 66, 77)( 67, 76)( 68, 75)( 69, 74)( 70, 73)( 71, 72)( 96,141)
( 97,140)( 98,139)( 99,138)(100,137)(101,136)(102,135)(103,134)(104,133)
(105,132)(106,131)(107,130)(108,129)(109,128)(110,127)(111,126)(112,125)
(113,124)(114,123)(115,122)(116,121)(117,120)(118,119)(143,188)(144,187)
(145,186)(146,185)(147,184)(148,183)(149,182)(150,181)(151,180)(152,179)
(153,178)(154,177)(155,176)(156,175)(157,174)(158,173)(159,172)(160,171)
(161,170)(162,169)(163,168)(164,167)(165,166)(190,235)(191,234)(192,233)
(193,232)(194,231)(195,230)(196,229)(197,228)(198,227)(199,226)(200,225)
(201,224)(202,223)(203,222)(204,221)(205,220)(206,219)(207,218)(208,217)
(209,216)(210,215)(211,214)(212,213)(237,282)(238,281)(239,280)(240,279)
(241,278)(242,277)(243,276)(244,275)(245,274)(246,273)(247,272)(248,271)
(249,270)(250,269)(251,268)(252,267)(253,266)(254,265)(255,264)(256,263)
(257,262)(258,261)(259,260)(284,329)(285,328)(286,327)(287,326)(288,325)
(289,324)(290,323)(291,322)(292,321)(293,320)(294,319)(295,318)(296,317)
(297,316)(298,315)(299,314)(300,313)(301,312)(302,311)(303,310)(304,309)
(305,308)(306,307)(331,376)(332,375)(333,374)(334,373)(335,372)(336,371)
(337,370)(338,369)(339,368)(340,367)(341,366)(342,365)(343,364)(344,363)
(345,362)(346,361)(347,360)(348,359)(349,358)(350,357)(351,356)(352,355)
(353,354)(378,423)(379,422)(380,421)(381,420)(382,419)(383,418)(384,417)
(385,416)(386,415)(387,414)(388,413)(389,412)(390,411)(391,410)(392,409)
(393,408)(394,407)(395,406)(396,405)(397,404)(398,403)(399,402)(400,401)
(425,470)(426,469)(427,468)(428,467)(429,466)(430,465)(431,464)(432,463)
(433,462)(434,461)(435,460)(436,459)(437,458)(438,457)(439,456)(440,455)
(441,454)(442,453)(443,452)(444,451)(445,450)(446,449)(447,448);
s1 := Sym(470)!( 1, 2)( 3, 47)( 4, 46)( 5, 45)( 6, 44)( 7, 43)( 8, 42)
( 9, 41)( 10, 40)( 11, 39)( 12, 38)( 13, 37)( 14, 36)( 15, 35)( 16, 34)
( 17, 33)( 18, 32)( 19, 31)( 20, 30)( 21, 29)( 22, 28)( 23, 27)( 24, 26)
( 48,190)( 49,189)( 50,235)( 51,234)( 52,233)( 53,232)( 54,231)( 55,230)
( 56,229)( 57,228)( 58,227)( 59,226)( 60,225)( 61,224)( 62,223)( 63,222)
( 64,221)( 65,220)( 66,219)( 67,218)( 68,217)( 69,216)( 70,215)( 71,214)
( 72,213)( 73,212)( 74,211)( 75,210)( 76,209)( 77,208)( 78,207)( 79,206)
( 80,205)( 81,204)( 82,203)( 83,202)( 84,201)( 85,200)( 86,199)( 87,198)
( 88,197)( 89,196)( 90,195)( 91,194)( 92,193)( 93,192)( 94,191)( 95,143)
( 96,142)( 97,188)( 98,187)( 99,186)(100,185)(101,184)(102,183)(103,182)
(104,181)(105,180)(106,179)(107,178)(108,177)(109,176)(110,175)(111,174)
(112,173)(113,172)(114,171)(115,170)(116,169)(117,168)(118,167)(119,166)
(120,165)(121,164)(122,163)(123,162)(124,161)(125,160)(126,159)(127,158)
(128,157)(129,156)(130,155)(131,154)(132,153)(133,152)(134,151)(135,150)
(136,149)(137,148)(138,147)(139,146)(140,145)(141,144)(236,237)(238,282)
(239,281)(240,280)(241,279)(242,278)(243,277)(244,276)(245,275)(246,274)
(247,273)(248,272)(249,271)(250,270)(251,269)(252,268)(253,267)(254,266)
(255,265)(256,264)(257,263)(258,262)(259,261)(283,425)(284,424)(285,470)
(286,469)(287,468)(288,467)(289,466)(290,465)(291,464)(292,463)(293,462)
(294,461)(295,460)(296,459)(297,458)(298,457)(299,456)(300,455)(301,454)
(302,453)(303,452)(304,451)(305,450)(306,449)(307,448)(308,447)(309,446)
(310,445)(311,444)(312,443)(313,442)(314,441)(315,440)(316,439)(317,438)
(318,437)(319,436)(320,435)(321,434)(322,433)(323,432)(324,431)(325,430)
(326,429)(327,428)(328,427)(329,426)(330,378)(331,377)(332,423)(333,422)
(334,421)(335,420)(336,419)(337,418)(338,417)(339,416)(340,415)(341,414)
(342,413)(343,412)(344,411)(345,410)(346,409)(347,408)(348,407)(349,406)
(350,405)(351,404)(352,403)(353,402)(354,401)(355,400)(356,399)(357,398)
(358,397)(359,396)(360,395)(361,394)(362,393)(363,392)(364,391)(365,390)
(366,389)(367,388)(368,387)(369,386)(370,385)(371,384)(372,383)(373,382)
(374,381)(375,380)(376,379);
s2 := Sym(470)!( 1,283)( 2,284)( 3,285)( 4,286)( 5,287)( 6,288)( 7,289)
( 8,290)( 9,291)( 10,292)( 11,293)( 12,294)( 13,295)( 14,296)( 15,297)
( 16,298)( 17,299)( 18,300)( 19,301)( 20,302)( 21,303)( 22,304)( 23,305)
( 24,306)( 25,307)( 26,308)( 27,309)( 28,310)( 29,311)( 30,312)( 31,313)
( 32,314)( 33,315)( 34,316)( 35,317)( 36,318)( 37,319)( 38,320)( 39,321)
( 40,322)( 41,323)( 42,324)( 43,325)( 44,326)( 45,327)( 46,328)( 47,329)
( 48,236)( 49,237)( 50,238)( 51,239)( 52,240)( 53,241)( 54,242)( 55,243)
( 56,244)( 57,245)( 58,246)( 59,247)( 60,248)( 61,249)( 62,250)( 63,251)
( 64,252)( 65,253)( 66,254)( 67,255)( 68,256)( 69,257)( 70,258)( 71,259)
( 72,260)( 73,261)( 74,262)( 75,263)( 76,264)( 77,265)( 78,266)( 79,267)
( 80,268)( 81,269)( 82,270)( 83,271)( 84,272)( 85,273)( 86,274)( 87,275)
( 88,276)( 89,277)( 90,278)( 91,279)( 92,280)( 93,281)( 94,282)( 95,424)
( 96,425)( 97,426)( 98,427)( 99,428)(100,429)(101,430)(102,431)(103,432)
(104,433)(105,434)(106,435)(107,436)(108,437)(109,438)(110,439)(111,440)
(112,441)(113,442)(114,443)(115,444)(116,445)(117,446)(118,447)(119,448)
(120,449)(121,450)(122,451)(123,452)(124,453)(125,454)(126,455)(127,456)
(128,457)(129,458)(130,459)(131,460)(132,461)(133,462)(134,463)(135,464)
(136,465)(137,466)(138,467)(139,468)(140,469)(141,470)(142,377)(143,378)
(144,379)(145,380)(146,381)(147,382)(148,383)(149,384)(150,385)(151,386)
(152,387)(153,388)(154,389)(155,390)(156,391)(157,392)(158,393)(159,394)
(160,395)(161,396)(162,397)(163,398)(164,399)(165,400)(166,401)(167,402)
(168,403)(169,404)(170,405)(171,406)(172,407)(173,408)(174,409)(175,410)
(176,411)(177,412)(178,413)(179,414)(180,415)(181,416)(182,417)(183,418)
(184,419)(185,420)(186,421)(187,422)(188,423)(189,330)(190,331)(191,332)
(192,333)(193,334)(194,335)(195,336)(196,337)(197,338)(198,339)(199,340)
(200,341)(201,342)(202,343)(203,344)(204,345)(205,346)(206,347)(207,348)
(208,349)(209,350)(210,351)(211,352)(212,353)(213,354)(214,355)(215,356)
(216,357)(217,358)(218,359)(219,360)(220,361)(221,362)(222,363)(223,364)
(224,365)(225,366)(226,367)(227,368)(228,369)(229,370)(230,371)(231,372)
(232,373)(233,374)(234,375)(235,376);
poly := sub<Sym(470)|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*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*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