Polytope of Type {20,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,10}*2000c
if this polytope has a name.
Group : SmallGroup(2000,395)
Rank : 3
Schlafli Type : {20,10}
Number of vertices, edges, etc : 100, 500, 50
Order of s0s1s2 : 20
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {10,10}*1000b
4-fold quotients : {10,5}*500
5-fold quotients : {20,10}*400c
10-fold quotients : {10,10}*200b
20-fold quotients : {10,5}*100
25-fold quotients : {4,10}*80
50-fold quotients : {2,10}*40
100-fold quotients : {2,5}*20
125-fold quotients : {4,2}*16
250-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 26,101)( 27,105)( 28,104)( 29,103)( 30,102)( 31,106)
( 32,110)( 33,109)( 34,108)( 35,107)( 36,111)( 37,115)( 38,114)( 39,113)
( 40,112)( 41,116)( 42,120)( 43,119)( 44,118)( 45,117)( 46,121)( 47,125)
( 48,124)( 49,123)( 50,122)( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)
( 56, 81)( 57, 85)( 58, 84)( 59, 83)( 60, 82)( 61, 86)( 62, 90)( 63, 89)
( 64, 88)( 65, 87)( 66, 91)( 67, 95)( 68, 94)( 69, 93)( 70, 92)( 71, 96)
( 72,100)( 73, 99)( 74, 98)( 75, 97)(127,130)(128,129)(132,135)(133,134)
(137,140)(138,139)(142,145)(143,144)(147,150)(148,149)(151,226)(152,230)
(153,229)(154,228)(155,227)(156,231)(157,235)(158,234)(159,233)(160,232)
(161,236)(162,240)(163,239)(164,238)(165,237)(166,241)(167,245)(168,244)
(169,243)(170,242)(171,246)(172,250)(173,249)(174,248)(175,247)(176,201)
(177,205)(178,204)(179,203)(180,202)(181,206)(182,210)(183,209)(184,208)
(185,207)(186,211)(187,215)(188,214)(189,213)(190,212)(191,216)(192,220)
(193,219)(194,218)(195,217)(196,221)(197,225)(198,224)(199,223)(200,222)
(251,376)(252,380)(253,379)(254,378)(255,377)(256,381)(257,385)(258,384)
(259,383)(260,382)(261,386)(262,390)(263,389)(264,388)(265,387)(266,391)
(267,395)(268,394)(269,393)(270,392)(271,396)(272,400)(273,399)(274,398)
(275,397)(276,476)(277,480)(278,479)(279,478)(280,477)(281,481)(282,485)
(283,484)(284,483)(285,482)(286,486)(287,490)(288,489)(289,488)(290,487)
(291,491)(292,495)(293,494)(294,493)(295,492)(296,496)(297,500)(298,499)
(299,498)(300,497)(301,451)(302,455)(303,454)(304,453)(305,452)(306,456)
(307,460)(308,459)(309,458)(310,457)(311,461)(312,465)(313,464)(314,463)
(315,462)(316,466)(317,470)(318,469)(319,468)(320,467)(321,471)(322,475)
(323,474)(324,473)(325,472)(326,426)(327,430)(328,429)(329,428)(330,427)
(331,431)(332,435)(333,434)(334,433)(335,432)(336,436)(337,440)(338,439)
(339,438)(340,437)(341,441)(342,445)(343,444)(344,443)(345,442)(346,446)
(347,450)(348,449)(349,448)(350,447)(351,401)(352,405)(353,404)(354,403)
(355,402)(356,406)(357,410)(358,409)(359,408)(360,407)(361,411)(362,415)
(363,414)(364,413)(365,412)(366,416)(367,420)(368,419)(369,418)(370,417)
(371,421)(372,425)(373,424)(374,423)(375,422);;
s1 := ( 1,276)( 2,277)( 3,278)( 4,279)( 5,280)( 6,300)( 7,296)( 8,297)
( 9,298)( 10,299)( 11,294)( 12,295)( 13,291)( 14,292)( 15,293)( 16,288)
( 17,289)( 18,290)( 19,286)( 20,287)( 21,282)( 22,283)( 23,284)( 24,285)
( 25,281)( 26,251)( 27,252)( 28,253)( 29,254)( 30,255)( 31,275)( 32,271)
( 33,272)( 34,273)( 35,274)( 36,269)( 37,270)( 38,266)( 39,267)( 40,268)
( 41,263)( 42,264)( 43,265)( 44,261)( 45,262)( 46,257)( 47,258)( 48,259)
( 49,260)( 50,256)( 51,351)( 52,352)( 53,353)( 54,354)( 55,355)( 56,375)
( 57,371)( 58,372)( 59,373)( 60,374)( 61,369)( 62,370)( 63,366)( 64,367)
( 65,368)( 66,363)( 67,364)( 68,365)( 69,361)( 70,362)( 71,357)( 72,358)
( 73,359)( 74,360)( 75,356)( 76,326)( 77,327)( 78,328)( 79,329)( 80,330)
( 81,350)( 82,346)( 83,347)( 84,348)( 85,349)( 86,344)( 87,345)( 88,341)
( 89,342)( 90,343)( 91,338)( 92,339)( 93,340)( 94,336)( 95,337)( 96,332)
( 97,333)( 98,334)( 99,335)(100,331)(101,301)(102,302)(103,303)(104,304)
(105,305)(106,325)(107,321)(108,322)(109,323)(110,324)(111,319)(112,320)
(113,316)(114,317)(115,318)(116,313)(117,314)(118,315)(119,311)(120,312)
(121,307)(122,308)(123,309)(124,310)(125,306)(126,401)(127,402)(128,403)
(129,404)(130,405)(131,425)(132,421)(133,422)(134,423)(135,424)(136,419)
(137,420)(138,416)(139,417)(140,418)(141,413)(142,414)(143,415)(144,411)
(145,412)(146,407)(147,408)(148,409)(149,410)(150,406)(151,376)(152,377)
(153,378)(154,379)(155,380)(156,400)(157,396)(158,397)(159,398)(160,399)
(161,394)(162,395)(163,391)(164,392)(165,393)(166,388)(167,389)(168,390)
(169,386)(170,387)(171,382)(172,383)(173,384)(174,385)(175,381)(176,476)
(177,477)(178,478)(179,479)(180,480)(181,500)(182,496)(183,497)(184,498)
(185,499)(186,494)(187,495)(188,491)(189,492)(190,493)(191,488)(192,489)
(193,490)(194,486)(195,487)(196,482)(197,483)(198,484)(199,485)(200,481)
(201,451)(202,452)(203,453)(204,454)(205,455)(206,475)(207,471)(208,472)
(209,473)(210,474)(211,469)(212,470)(213,466)(214,467)(215,468)(216,463)
(217,464)(218,465)(219,461)(220,462)(221,457)(222,458)(223,459)(224,460)
(225,456)(226,426)(227,427)(228,428)(229,429)(230,430)(231,450)(232,446)
(233,447)(234,448)(235,449)(236,444)(237,445)(238,441)(239,442)(240,443)
(241,438)(242,439)(243,440)(244,436)(245,437)(246,432)(247,433)(248,434)
(249,435)(250,431);;
s2 := ( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5, 10)( 11, 21)( 12, 22)( 13, 23)
( 14, 24)( 15, 25)( 26,106)( 27,107)( 28,108)( 29,109)( 30,110)( 31,101)
( 32,102)( 33,103)( 34,104)( 35,105)( 36,121)( 37,122)( 38,123)( 39,124)
( 40,125)( 41,116)( 42,117)( 43,118)( 44,119)( 45,120)( 46,111)( 47,112)
( 48,113)( 49,114)( 50,115)( 51, 81)( 52, 82)( 53, 83)( 54, 84)( 55, 85)
( 56, 76)( 57, 77)( 58, 78)( 59, 79)( 60, 80)( 61, 96)( 62, 97)( 63, 98)
( 64, 99)( 65,100)( 66, 91)( 67, 92)( 68, 93)( 69, 94)( 70, 95)( 71, 86)
( 72, 87)( 73, 88)( 74, 89)( 75, 90)(126,131)(127,132)(128,133)(129,134)
(130,135)(136,146)(137,147)(138,148)(139,149)(140,150)(151,231)(152,232)
(153,233)(154,234)(155,235)(156,226)(157,227)(158,228)(159,229)(160,230)
(161,246)(162,247)(163,248)(164,249)(165,250)(166,241)(167,242)(168,243)
(169,244)(170,245)(171,236)(172,237)(173,238)(174,239)(175,240)(176,206)
(177,207)(178,208)(179,209)(180,210)(181,201)(182,202)(183,203)(184,204)
(185,205)(186,221)(187,222)(188,223)(189,224)(190,225)(191,216)(192,217)
(193,218)(194,219)(195,220)(196,211)(197,212)(198,213)(199,214)(200,215)
(251,256)(252,257)(253,258)(254,259)(255,260)(261,271)(262,272)(263,273)
(264,274)(265,275)(276,356)(277,357)(278,358)(279,359)(280,360)(281,351)
(282,352)(283,353)(284,354)(285,355)(286,371)(287,372)(288,373)(289,374)
(290,375)(291,366)(292,367)(293,368)(294,369)(295,370)(296,361)(297,362)
(298,363)(299,364)(300,365)(301,331)(302,332)(303,333)(304,334)(305,335)
(306,326)(307,327)(308,328)(309,329)(310,330)(311,346)(312,347)(313,348)
(314,349)(315,350)(316,341)(317,342)(318,343)(319,344)(320,345)(321,336)
(322,337)(323,338)(324,339)(325,340)(376,381)(377,382)(378,383)(379,384)
(380,385)(386,396)(387,397)(388,398)(389,399)(390,400)(401,481)(402,482)
(403,483)(404,484)(405,485)(406,476)(407,477)(408,478)(409,479)(410,480)
(411,496)(412,497)(413,498)(414,499)(415,500)(416,491)(417,492)(418,493)
(419,494)(420,495)(421,486)(422,487)(423,488)(424,489)(425,490)(426,456)
(427,457)(428,458)(429,459)(430,460)(431,451)(432,452)(433,453)(434,454)
(435,455)(436,471)(437,472)(438,473)(439,474)(440,475)(441,466)(442,467)
(443,468)(444,469)(445,470)(446,461)(447,462)(448,463)(449,464)(450,465);;
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*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s1*s2*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(500)!( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 22, 25)( 23, 24)( 26,101)( 27,105)( 28,104)( 29,103)( 30,102)
( 31,106)( 32,110)( 33,109)( 34,108)( 35,107)( 36,111)( 37,115)( 38,114)
( 39,113)( 40,112)( 41,116)( 42,120)( 43,119)( 44,118)( 45,117)( 46,121)
( 47,125)( 48,124)( 49,123)( 50,122)( 51, 76)( 52, 80)( 53, 79)( 54, 78)
( 55, 77)( 56, 81)( 57, 85)( 58, 84)( 59, 83)( 60, 82)( 61, 86)( 62, 90)
( 63, 89)( 64, 88)( 65, 87)( 66, 91)( 67, 95)( 68, 94)( 69, 93)( 70, 92)
( 71, 96)( 72,100)( 73, 99)( 74, 98)( 75, 97)(127,130)(128,129)(132,135)
(133,134)(137,140)(138,139)(142,145)(143,144)(147,150)(148,149)(151,226)
(152,230)(153,229)(154,228)(155,227)(156,231)(157,235)(158,234)(159,233)
(160,232)(161,236)(162,240)(163,239)(164,238)(165,237)(166,241)(167,245)
(168,244)(169,243)(170,242)(171,246)(172,250)(173,249)(174,248)(175,247)
(176,201)(177,205)(178,204)(179,203)(180,202)(181,206)(182,210)(183,209)
(184,208)(185,207)(186,211)(187,215)(188,214)(189,213)(190,212)(191,216)
(192,220)(193,219)(194,218)(195,217)(196,221)(197,225)(198,224)(199,223)
(200,222)(251,376)(252,380)(253,379)(254,378)(255,377)(256,381)(257,385)
(258,384)(259,383)(260,382)(261,386)(262,390)(263,389)(264,388)(265,387)
(266,391)(267,395)(268,394)(269,393)(270,392)(271,396)(272,400)(273,399)
(274,398)(275,397)(276,476)(277,480)(278,479)(279,478)(280,477)(281,481)
(282,485)(283,484)(284,483)(285,482)(286,486)(287,490)(288,489)(289,488)
(290,487)(291,491)(292,495)(293,494)(294,493)(295,492)(296,496)(297,500)
(298,499)(299,498)(300,497)(301,451)(302,455)(303,454)(304,453)(305,452)
(306,456)(307,460)(308,459)(309,458)(310,457)(311,461)(312,465)(313,464)
(314,463)(315,462)(316,466)(317,470)(318,469)(319,468)(320,467)(321,471)
(322,475)(323,474)(324,473)(325,472)(326,426)(327,430)(328,429)(329,428)
(330,427)(331,431)(332,435)(333,434)(334,433)(335,432)(336,436)(337,440)
(338,439)(339,438)(340,437)(341,441)(342,445)(343,444)(344,443)(345,442)
(346,446)(347,450)(348,449)(349,448)(350,447)(351,401)(352,405)(353,404)
(354,403)(355,402)(356,406)(357,410)(358,409)(359,408)(360,407)(361,411)
(362,415)(363,414)(364,413)(365,412)(366,416)(367,420)(368,419)(369,418)
(370,417)(371,421)(372,425)(373,424)(374,423)(375,422);
s1 := Sym(500)!( 1,276)( 2,277)( 3,278)( 4,279)( 5,280)( 6,300)( 7,296)
( 8,297)( 9,298)( 10,299)( 11,294)( 12,295)( 13,291)( 14,292)( 15,293)
( 16,288)( 17,289)( 18,290)( 19,286)( 20,287)( 21,282)( 22,283)( 23,284)
( 24,285)( 25,281)( 26,251)( 27,252)( 28,253)( 29,254)( 30,255)( 31,275)
( 32,271)( 33,272)( 34,273)( 35,274)( 36,269)( 37,270)( 38,266)( 39,267)
( 40,268)( 41,263)( 42,264)( 43,265)( 44,261)( 45,262)( 46,257)( 47,258)
( 48,259)( 49,260)( 50,256)( 51,351)( 52,352)( 53,353)( 54,354)( 55,355)
( 56,375)( 57,371)( 58,372)( 59,373)( 60,374)( 61,369)( 62,370)( 63,366)
( 64,367)( 65,368)( 66,363)( 67,364)( 68,365)( 69,361)( 70,362)( 71,357)
( 72,358)( 73,359)( 74,360)( 75,356)( 76,326)( 77,327)( 78,328)( 79,329)
( 80,330)( 81,350)( 82,346)( 83,347)( 84,348)( 85,349)( 86,344)( 87,345)
( 88,341)( 89,342)( 90,343)( 91,338)( 92,339)( 93,340)( 94,336)( 95,337)
( 96,332)( 97,333)( 98,334)( 99,335)(100,331)(101,301)(102,302)(103,303)
(104,304)(105,305)(106,325)(107,321)(108,322)(109,323)(110,324)(111,319)
(112,320)(113,316)(114,317)(115,318)(116,313)(117,314)(118,315)(119,311)
(120,312)(121,307)(122,308)(123,309)(124,310)(125,306)(126,401)(127,402)
(128,403)(129,404)(130,405)(131,425)(132,421)(133,422)(134,423)(135,424)
(136,419)(137,420)(138,416)(139,417)(140,418)(141,413)(142,414)(143,415)
(144,411)(145,412)(146,407)(147,408)(148,409)(149,410)(150,406)(151,376)
(152,377)(153,378)(154,379)(155,380)(156,400)(157,396)(158,397)(159,398)
(160,399)(161,394)(162,395)(163,391)(164,392)(165,393)(166,388)(167,389)
(168,390)(169,386)(170,387)(171,382)(172,383)(173,384)(174,385)(175,381)
(176,476)(177,477)(178,478)(179,479)(180,480)(181,500)(182,496)(183,497)
(184,498)(185,499)(186,494)(187,495)(188,491)(189,492)(190,493)(191,488)
(192,489)(193,490)(194,486)(195,487)(196,482)(197,483)(198,484)(199,485)
(200,481)(201,451)(202,452)(203,453)(204,454)(205,455)(206,475)(207,471)
(208,472)(209,473)(210,474)(211,469)(212,470)(213,466)(214,467)(215,468)
(216,463)(217,464)(218,465)(219,461)(220,462)(221,457)(222,458)(223,459)
(224,460)(225,456)(226,426)(227,427)(228,428)(229,429)(230,430)(231,450)
(232,446)(233,447)(234,448)(235,449)(236,444)(237,445)(238,441)(239,442)
(240,443)(241,438)(242,439)(243,440)(244,436)(245,437)(246,432)(247,433)
(248,434)(249,435)(250,431);
s2 := Sym(500)!( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5, 10)( 11, 21)( 12, 22)
( 13, 23)( 14, 24)( 15, 25)( 26,106)( 27,107)( 28,108)( 29,109)( 30,110)
( 31,101)( 32,102)( 33,103)( 34,104)( 35,105)( 36,121)( 37,122)( 38,123)
( 39,124)( 40,125)( 41,116)( 42,117)( 43,118)( 44,119)( 45,120)( 46,111)
( 47,112)( 48,113)( 49,114)( 50,115)( 51, 81)( 52, 82)( 53, 83)( 54, 84)
( 55, 85)( 56, 76)( 57, 77)( 58, 78)( 59, 79)( 60, 80)( 61, 96)( 62, 97)
( 63, 98)( 64, 99)( 65,100)( 66, 91)( 67, 92)( 68, 93)( 69, 94)( 70, 95)
( 71, 86)( 72, 87)( 73, 88)( 74, 89)( 75, 90)(126,131)(127,132)(128,133)
(129,134)(130,135)(136,146)(137,147)(138,148)(139,149)(140,150)(151,231)
(152,232)(153,233)(154,234)(155,235)(156,226)(157,227)(158,228)(159,229)
(160,230)(161,246)(162,247)(163,248)(164,249)(165,250)(166,241)(167,242)
(168,243)(169,244)(170,245)(171,236)(172,237)(173,238)(174,239)(175,240)
(176,206)(177,207)(178,208)(179,209)(180,210)(181,201)(182,202)(183,203)
(184,204)(185,205)(186,221)(187,222)(188,223)(189,224)(190,225)(191,216)
(192,217)(193,218)(194,219)(195,220)(196,211)(197,212)(198,213)(199,214)
(200,215)(251,256)(252,257)(253,258)(254,259)(255,260)(261,271)(262,272)
(263,273)(264,274)(265,275)(276,356)(277,357)(278,358)(279,359)(280,360)
(281,351)(282,352)(283,353)(284,354)(285,355)(286,371)(287,372)(288,373)
(289,374)(290,375)(291,366)(292,367)(293,368)(294,369)(295,370)(296,361)
(297,362)(298,363)(299,364)(300,365)(301,331)(302,332)(303,333)(304,334)
(305,335)(306,326)(307,327)(308,328)(309,329)(310,330)(311,346)(312,347)
(313,348)(314,349)(315,350)(316,341)(317,342)(318,343)(319,344)(320,345)
(321,336)(322,337)(323,338)(324,339)(325,340)(376,381)(377,382)(378,383)
(379,384)(380,385)(386,396)(387,397)(388,398)(389,399)(390,400)(401,481)
(402,482)(403,483)(404,484)(405,485)(406,476)(407,477)(408,478)(409,479)
(410,480)(411,496)(412,497)(413,498)(414,499)(415,500)(416,491)(417,492)
(418,493)(419,494)(420,495)(421,486)(422,487)(423,488)(424,489)(425,490)
(426,456)(427,457)(428,458)(429,459)(430,460)(431,451)(432,452)(433,453)
(434,454)(435,455)(436,471)(437,472)(438,473)(439,474)(440,475)(441,466)
(442,467)(443,468)(444,469)(445,470)(446,461)(447,462)(448,463)(449,464)
(450,465);
poly := sub<Sym(500)|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*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s1*s2*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope