Polytope of Type {4,51}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,51}*816
if this polytope has a name.
Group : SmallGroup(816,195)
Rank : 3
Schlafli Type : {4,51}
Number of vertices, edges, etc : 8, 204, 102
Order of s0s1s2 : 102
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,51,2} of size 1632
Vertex Figure Of :
{2,4,51} of size 1632
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,51}*408
4-fold quotients : {2,51}*204
12-fold quotients : {2,17}*68
17-fold quotients : {4,3}*48
34-fold quotients : {4,3}*24
68-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
2-fold covers : {8,51}*1632, {4,102}*1632
Permutation Representation (GAP) :
s0 := ( 1,207)( 2,208)( 3,205)( 4,206)( 5,211)( 6,212)( 7,209)( 8,210)
( 9,215)( 10,216)( 11,213)( 12,214)( 13,219)( 14,220)( 15,217)( 16,218)
( 17,223)( 18,224)( 19,221)( 20,222)( 21,227)( 22,228)( 23,225)( 24,226)
( 25,231)( 26,232)( 27,229)( 28,230)( 29,235)( 30,236)( 31,233)( 32,234)
( 33,239)( 34,240)( 35,237)( 36,238)( 37,243)( 38,244)( 39,241)( 40,242)
( 41,247)( 42,248)( 43,245)( 44,246)( 45,251)( 46,252)( 47,249)( 48,250)
( 49,255)( 50,256)( 51,253)( 52,254)( 53,259)( 54,260)( 55,257)( 56,258)
( 57,263)( 58,264)( 59,261)( 60,262)( 61,267)( 62,268)( 63,265)( 64,266)
( 65,271)( 66,272)( 67,269)( 68,270)( 69,275)( 70,276)( 71,273)( 72,274)
( 73,279)( 74,280)( 75,277)( 76,278)( 77,283)( 78,284)( 79,281)( 80,282)
( 81,287)( 82,288)( 83,285)( 84,286)( 85,291)( 86,292)( 87,289)( 88,290)
( 89,295)( 90,296)( 91,293)( 92,294)( 93,299)( 94,300)( 95,297)( 96,298)
( 97,303)( 98,304)( 99,301)(100,302)(101,307)(102,308)(103,305)(104,306)
(105,311)(106,312)(107,309)(108,310)(109,315)(110,316)(111,313)(112,314)
(113,319)(114,320)(115,317)(116,318)(117,323)(118,324)(119,321)(120,322)
(121,327)(122,328)(123,325)(124,326)(125,331)(126,332)(127,329)(128,330)
(129,335)(130,336)(131,333)(132,334)(133,339)(134,340)(135,337)(136,338)
(137,343)(138,344)(139,341)(140,342)(141,347)(142,348)(143,345)(144,346)
(145,351)(146,352)(147,349)(148,350)(149,355)(150,356)(151,353)(152,354)
(153,359)(154,360)(155,357)(156,358)(157,363)(158,364)(159,361)(160,362)
(161,367)(162,368)(163,365)(164,366)(165,371)(166,372)(167,369)(168,370)
(169,375)(170,376)(171,373)(172,374)(173,379)(174,380)(175,377)(176,378)
(177,383)(178,384)(179,381)(180,382)(181,387)(182,388)(183,385)(184,386)
(185,391)(186,392)(187,389)(188,390)(189,395)(190,396)(191,393)(192,394)
(193,399)(194,400)(195,397)(196,398)(197,403)(198,404)(199,401)(200,402)
(201,407)(202,408)(203,405)(204,406);;
s1 := ( 2, 3)( 5, 65)( 6, 67)( 7, 66)( 8, 68)( 9, 61)( 10, 63)( 11, 62)
( 12, 64)( 13, 57)( 14, 59)( 15, 58)( 16, 60)( 17, 53)( 18, 55)( 19, 54)
( 20, 56)( 21, 49)( 22, 51)( 23, 50)( 24, 52)( 25, 45)( 26, 47)( 27, 46)
( 28, 48)( 29, 41)( 30, 43)( 31, 42)( 32, 44)( 33, 37)( 34, 39)( 35, 38)
( 36, 40)( 69,137)( 70,139)( 71,138)( 72,140)( 73,201)( 74,203)( 75,202)
( 76,204)( 77,197)( 78,199)( 79,198)( 80,200)( 81,193)( 82,195)( 83,194)
( 84,196)( 85,189)( 86,191)( 87,190)( 88,192)( 89,185)( 90,187)( 91,186)
( 92,188)( 93,181)( 94,183)( 95,182)( 96,184)( 97,177)( 98,179)( 99,178)
(100,180)(101,173)(102,175)(103,174)(104,176)(105,169)(106,171)(107,170)
(108,172)(109,165)(110,167)(111,166)(112,168)(113,161)(114,163)(115,162)
(116,164)(117,157)(118,159)(119,158)(120,160)(121,153)(122,155)(123,154)
(124,156)(125,149)(126,151)(127,150)(128,152)(129,145)(130,147)(131,146)
(132,148)(133,141)(134,143)(135,142)(136,144)(206,207)(209,269)(210,271)
(211,270)(212,272)(213,265)(214,267)(215,266)(216,268)(217,261)(218,263)
(219,262)(220,264)(221,257)(222,259)(223,258)(224,260)(225,253)(226,255)
(227,254)(228,256)(229,249)(230,251)(231,250)(232,252)(233,245)(234,247)
(235,246)(236,248)(237,241)(238,243)(239,242)(240,244)(273,341)(274,343)
(275,342)(276,344)(277,405)(278,407)(279,406)(280,408)(281,401)(282,403)
(283,402)(284,404)(285,397)(286,399)(287,398)(288,400)(289,393)(290,395)
(291,394)(292,396)(293,389)(294,391)(295,390)(296,392)(297,385)(298,387)
(299,386)(300,388)(301,381)(302,383)(303,382)(304,384)(305,377)(306,379)
(307,378)(308,380)(309,373)(310,375)(311,374)(312,376)(313,369)(314,371)
(315,370)(316,372)(317,365)(318,367)(319,366)(320,368)(321,361)(322,363)
(323,362)(324,364)(325,357)(326,359)(327,358)(328,360)(329,353)(330,355)
(331,354)(332,356)(333,349)(334,351)(335,350)(336,352)(337,345)(338,347)
(339,346)(340,348);;
s2 := ( 1,141)( 2,144)( 3,143)( 4,142)( 5,137)( 6,140)( 7,139)( 8,138)
( 9,201)( 10,204)( 11,203)( 12,202)( 13,197)( 14,200)( 15,199)( 16,198)
( 17,193)( 18,196)( 19,195)( 20,194)( 21,189)( 22,192)( 23,191)( 24,190)
( 25,185)( 26,188)( 27,187)( 28,186)( 29,181)( 30,184)( 31,183)( 32,182)
( 33,177)( 34,180)( 35,179)( 36,178)( 37,173)( 38,176)( 39,175)( 40,174)
( 41,169)( 42,172)( 43,171)( 44,170)( 45,165)( 46,168)( 47,167)( 48,166)
( 49,161)( 50,164)( 51,163)( 52,162)( 53,157)( 54,160)( 55,159)( 56,158)
( 57,153)( 58,156)( 59,155)( 60,154)( 61,149)( 62,152)( 63,151)( 64,150)
( 65,145)( 66,148)( 67,147)( 68,146)( 69, 73)( 70, 76)( 71, 75)( 72, 74)
( 77,133)( 78,136)( 79,135)( 80,134)( 81,129)( 82,132)( 83,131)( 84,130)
( 85,125)( 86,128)( 87,127)( 88,126)( 89,121)( 90,124)( 91,123)( 92,122)
( 93,117)( 94,120)( 95,119)( 96,118)( 97,113)( 98,116)( 99,115)(100,114)
(101,109)(102,112)(103,111)(104,110)(106,108)(205,345)(206,348)(207,347)
(208,346)(209,341)(210,344)(211,343)(212,342)(213,405)(214,408)(215,407)
(216,406)(217,401)(218,404)(219,403)(220,402)(221,397)(222,400)(223,399)
(224,398)(225,393)(226,396)(227,395)(228,394)(229,389)(230,392)(231,391)
(232,390)(233,385)(234,388)(235,387)(236,386)(237,381)(238,384)(239,383)
(240,382)(241,377)(242,380)(243,379)(244,378)(245,373)(246,376)(247,375)
(248,374)(249,369)(250,372)(251,371)(252,370)(253,365)(254,368)(255,367)
(256,366)(257,361)(258,364)(259,363)(260,362)(261,357)(262,360)(263,359)
(264,358)(265,353)(266,356)(267,355)(268,354)(269,349)(270,352)(271,351)
(272,350)(273,277)(274,280)(275,279)(276,278)(281,337)(282,340)(283,339)
(284,338)(285,333)(286,336)(287,335)(288,334)(289,329)(290,332)(291,331)
(292,330)(293,325)(294,328)(295,327)(296,326)(297,321)(298,324)(299,323)
(300,322)(301,317)(302,320)(303,319)(304,318)(305,313)(306,316)(307,315)
(308,314)(310,312);;
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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(408)!( 1,207)( 2,208)( 3,205)( 4,206)( 5,211)( 6,212)( 7,209)
( 8,210)( 9,215)( 10,216)( 11,213)( 12,214)( 13,219)( 14,220)( 15,217)
( 16,218)( 17,223)( 18,224)( 19,221)( 20,222)( 21,227)( 22,228)( 23,225)
( 24,226)( 25,231)( 26,232)( 27,229)( 28,230)( 29,235)( 30,236)( 31,233)
( 32,234)( 33,239)( 34,240)( 35,237)( 36,238)( 37,243)( 38,244)( 39,241)
( 40,242)( 41,247)( 42,248)( 43,245)( 44,246)( 45,251)( 46,252)( 47,249)
( 48,250)( 49,255)( 50,256)( 51,253)( 52,254)( 53,259)( 54,260)( 55,257)
( 56,258)( 57,263)( 58,264)( 59,261)( 60,262)( 61,267)( 62,268)( 63,265)
( 64,266)( 65,271)( 66,272)( 67,269)( 68,270)( 69,275)( 70,276)( 71,273)
( 72,274)( 73,279)( 74,280)( 75,277)( 76,278)( 77,283)( 78,284)( 79,281)
( 80,282)( 81,287)( 82,288)( 83,285)( 84,286)( 85,291)( 86,292)( 87,289)
( 88,290)( 89,295)( 90,296)( 91,293)( 92,294)( 93,299)( 94,300)( 95,297)
( 96,298)( 97,303)( 98,304)( 99,301)(100,302)(101,307)(102,308)(103,305)
(104,306)(105,311)(106,312)(107,309)(108,310)(109,315)(110,316)(111,313)
(112,314)(113,319)(114,320)(115,317)(116,318)(117,323)(118,324)(119,321)
(120,322)(121,327)(122,328)(123,325)(124,326)(125,331)(126,332)(127,329)
(128,330)(129,335)(130,336)(131,333)(132,334)(133,339)(134,340)(135,337)
(136,338)(137,343)(138,344)(139,341)(140,342)(141,347)(142,348)(143,345)
(144,346)(145,351)(146,352)(147,349)(148,350)(149,355)(150,356)(151,353)
(152,354)(153,359)(154,360)(155,357)(156,358)(157,363)(158,364)(159,361)
(160,362)(161,367)(162,368)(163,365)(164,366)(165,371)(166,372)(167,369)
(168,370)(169,375)(170,376)(171,373)(172,374)(173,379)(174,380)(175,377)
(176,378)(177,383)(178,384)(179,381)(180,382)(181,387)(182,388)(183,385)
(184,386)(185,391)(186,392)(187,389)(188,390)(189,395)(190,396)(191,393)
(192,394)(193,399)(194,400)(195,397)(196,398)(197,403)(198,404)(199,401)
(200,402)(201,407)(202,408)(203,405)(204,406);
s1 := Sym(408)!( 2, 3)( 5, 65)( 6, 67)( 7, 66)( 8, 68)( 9, 61)( 10, 63)
( 11, 62)( 12, 64)( 13, 57)( 14, 59)( 15, 58)( 16, 60)( 17, 53)( 18, 55)
( 19, 54)( 20, 56)( 21, 49)( 22, 51)( 23, 50)( 24, 52)( 25, 45)( 26, 47)
( 27, 46)( 28, 48)( 29, 41)( 30, 43)( 31, 42)( 32, 44)( 33, 37)( 34, 39)
( 35, 38)( 36, 40)( 69,137)( 70,139)( 71,138)( 72,140)( 73,201)( 74,203)
( 75,202)( 76,204)( 77,197)( 78,199)( 79,198)( 80,200)( 81,193)( 82,195)
( 83,194)( 84,196)( 85,189)( 86,191)( 87,190)( 88,192)( 89,185)( 90,187)
( 91,186)( 92,188)( 93,181)( 94,183)( 95,182)( 96,184)( 97,177)( 98,179)
( 99,178)(100,180)(101,173)(102,175)(103,174)(104,176)(105,169)(106,171)
(107,170)(108,172)(109,165)(110,167)(111,166)(112,168)(113,161)(114,163)
(115,162)(116,164)(117,157)(118,159)(119,158)(120,160)(121,153)(122,155)
(123,154)(124,156)(125,149)(126,151)(127,150)(128,152)(129,145)(130,147)
(131,146)(132,148)(133,141)(134,143)(135,142)(136,144)(206,207)(209,269)
(210,271)(211,270)(212,272)(213,265)(214,267)(215,266)(216,268)(217,261)
(218,263)(219,262)(220,264)(221,257)(222,259)(223,258)(224,260)(225,253)
(226,255)(227,254)(228,256)(229,249)(230,251)(231,250)(232,252)(233,245)
(234,247)(235,246)(236,248)(237,241)(238,243)(239,242)(240,244)(273,341)
(274,343)(275,342)(276,344)(277,405)(278,407)(279,406)(280,408)(281,401)
(282,403)(283,402)(284,404)(285,397)(286,399)(287,398)(288,400)(289,393)
(290,395)(291,394)(292,396)(293,389)(294,391)(295,390)(296,392)(297,385)
(298,387)(299,386)(300,388)(301,381)(302,383)(303,382)(304,384)(305,377)
(306,379)(307,378)(308,380)(309,373)(310,375)(311,374)(312,376)(313,369)
(314,371)(315,370)(316,372)(317,365)(318,367)(319,366)(320,368)(321,361)
(322,363)(323,362)(324,364)(325,357)(326,359)(327,358)(328,360)(329,353)
(330,355)(331,354)(332,356)(333,349)(334,351)(335,350)(336,352)(337,345)
(338,347)(339,346)(340,348);
s2 := Sym(408)!( 1,141)( 2,144)( 3,143)( 4,142)( 5,137)( 6,140)( 7,139)
( 8,138)( 9,201)( 10,204)( 11,203)( 12,202)( 13,197)( 14,200)( 15,199)
( 16,198)( 17,193)( 18,196)( 19,195)( 20,194)( 21,189)( 22,192)( 23,191)
( 24,190)( 25,185)( 26,188)( 27,187)( 28,186)( 29,181)( 30,184)( 31,183)
( 32,182)( 33,177)( 34,180)( 35,179)( 36,178)( 37,173)( 38,176)( 39,175)
( 40,174)( 41,169)( 42,172)( 43,171)( 44,170)( 45,165)( 46,168)( 47,167)
( 48,166)( 49,161)( 50,164)( 51,163)( 52,162)( 53,157)( 54,160)( 55,159)
( 56,158)( 57,153)( 58,156)( 59,155)( 60,154)( 61,149)( 62,152)( 63,151)
( 64,150)( 65,145)( 66,148)( 67,147)( 68,146)( 69, 73)( 70, 76)( 71, 75)
( 72, 74)( 77,133)( 78,136)( 79,135)( 80,134)( 81,129)( 82,132)( 83,131)
( 84,130)( 85,125)( 86,128)( 87,127)( 88,126)( 89,121)( 90,124)( 91,123)
( 92,122)( 93,117)( 94,120)( 95,119)( 96,118)( 97,113)( 98,116)( 99,115)
(100,114)(101,109)(102,112)(103,111)(104,110)(106,108)(205,345)(206,348)
(207,347)(208,346)(209,341)(210,344)(211,343)(212,342)(213,405)(214,408)
(215,407)(216,406)(217,401)(218,404)(219,403)(220,402)(221,397)(222,400)
(223,399)(224,398)(225,393)(226,396)(227,395)(228,394)(229,389)(230,392)
(231,391)(232,390)(233,385)(234,388)(235,387)(236,386)(237,381)(238,384)
(239,383)(240,382)(241,377)(242,380)(243,379)(244,378)(245,373)(246,376)
(247,375)(248,374)(249,369)(250,372)(251,371)(252,370)(253,365)(254,368)
(255,367)(256,366)(257,361)(258,364)(259,363)(260,362)(261,357)(262,360)
(263,359)(264,358)(265,353)(266,356)(267,355)(268,354)(269,349)(270,352)
(271,351)(272,350)(273,277)(274,280)(275,279)(276,278)(281,337)(282,340)
(283,339)(284,338)(285,333)(286,336)(287,335)(288,334)(289,329)(290,332)
(291,331)(292,330)(293,325)(294,328)(295,327)(296,326)(297,321)(298,324)
(299,323)(300,322)(301,317)(302,320)(303,319)(304,318)(305,313)(306,316)
(307,315)(308,314)(310,312);
poly := sub<Sym(408)|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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*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 >;
References : None.
to this polytope