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