Polytope of Type {51,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {51,4}*816
if this polytope has a name.
Group : SmallGroup(816,195)
Rank : 3
Schlafli Type : {51,4}
Number of vertices, edges, etc : 102, 204, 8
Order of s0s1s2 : 102
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
{51,4,2} of size 1632
Vertex Figure Of :
{2,51,4} of size 1632
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {51,4}*408
4-fold quotients : {51,2}*204
12-fold quotients : {17,2}*68
17-fold quotients : {3,4}*48
34-fold quotients : {3,4}*24
68-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
2-fold covers : {51,8}*1632, {102,4}*1632
Permutation Representation (GAP) :
s0 := ( 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);;
s1 := ( 1, 73)( 2, 74)( 3, 76)( 4, 75)( 5, 69)( 6, 70)( 7, 72)( 8, 71)
( 9,133)( 10,134)( 11,136)( 12,135)( 13,129)( 14,130)( 15,132)( 16,131)
( 17,125)( 18,126)( 19,128)( 20,127)( 21,121)( 22,122)( 23,124)( 24,123)
( 25,117)( 26,118)( 27,120)( 28,119)( 29,113)( 30,114)( 31,116)( 32,115)
( 33,109)( 34,110)( 35,112)( 36,111)( 37,105)( 38,106)( 39,108)( 40,107)
( 41,101)( 42,102)( 43,104)( 44,103)( 45, 97)( 46, 98)( 47,100)( 48, 99)
( 49, 93)( 50, 94)( 51, 96)( 52, 95)( 53, 89)( 54, 90)( 55, 92)( 56, 91)
( 57, 85)( 58, 86)( 59, 88)( 60, 87)( 61, 81)( 62, 82)( 63, 84)( 64, 83)
( 65, 77)( 66, 78)( 67, 80)( 68, 79)(137,141)(138,142)(139,144)(140,143)
(145,201)(146,202)(147,204)(148,203)(149,197)(150,198)(151,200)(152,199)
(153,193)(154,194)(155,196)(156,195)(157,189)(158,190)(159,192)(160,191)
(161,185)(162,186)(163,188)(164,187)(165,181)(166,182)(167,184)(168,183)
(169,177)(170,178)(171,180)(172,179)(175,176)(205,277)(206,278)(207,280)
(208,279)(209,273)(210,274)(211,276)(212,275)(213,337)(214,338)(215,340)
(216,339)(217,333)(218,334)(219,336)(220,335)(221,329)(222,330)(223,332)
(224,331)(225,325)(226,326)(227,328)(228,327)(229,321)(230,322)(231,324)
(232,323)(233,317)(234,318)(235,320)(236,319)(237,313)(238,314)(239,316)
(240,315)(241,309)(242,310)(243,312)(244,311)(245,305)(246,306)(247,308)
(248,307)(249,301)(250,302)(251,304)(252,303)(253,297)(254,298)(255,300)
(256,299)(257,293)(258,294)(259,296)(260,295)(261,289)(262,290)(263,292)
(264,291)(265,285)(266,286)(267,288)(268,287)(269,281)(270,282)(271,284)
(272,283)(341,345)(342,346)(343,348)(344,347)(349,405)(350,406)(351,408)
(352,407)(353,401)(354,402)(355,404)(356,403)(357,397)(358,398)(359,400)
(360,399)(361,393)(362,394)(363,396)(364,395)(365,389)(366,390)(367,392)
(368,391)(369,385)(370,386)(371,388)(372,387)(373,381)(374,382)(375,384)
(376,383)(379,380);;
s2 := ( 1,208)( 2,207)( 3,206)( 4,205)( 5,212)( 6,211)( 7,210)( 8,209)
( 9,216)( 10,215)( 11,214)( 12,213)( 13,220)( 14,219)( 15,218)( 16,217)
( 17,224)( 18,223)( 19,222)( 20,221)( 21,228)( 22,227)( 23,226)( 24,225)
( 25,232)( 26,231)( 27,230)( 28,229)( 29,236)( 30,235)( 31,234)( 32,233)
( 33,240)( 34,239)( 35,238)( 36,237)( 37,244)( 38,243)( 39,242)( 40,241)
( 41,248)( 42,247)( 43,246)( 44,245)( 45,252)( 46,251)( 47,250)( 48,249)
( 49,256)( 50,255)( 51,254)( 52,253)( 53,260)( 54,259)( 55,258)( 56,257)
( 57,264)( 58,263)( 59,262)( 60,261)( 61,268)( 62,267)( 63,266)( 64,265)
( 65,272)( 66,271)( 67,270)( 68,269)( 69,276)( 70,275)( 71,274)( 72,273)
( 73,280)( 74,279)( 75,278)( 76,277)( 77,284)( 78,283)( 79,282)( 80,281)
( 81,288)( 82,287)( 83,286)( 84,285)( 85,292)( 86,291)( 87,290)( 88,289)
( 89,296)( 90,295)( 91,294)( 92,293)( 93,300)( 94,299)( 95,298)( 96,297)
( 97,304)( 98,303)( 99,302)(100,301)(101,308)(102,307)(103,306)(104,305)
(105,312)(106,311)(107,310)(108,309)(109,316)(110,315)(111,314)(112,313)
(113,320)(114,319)(115,318)(116,317)(117,324)(118,323)(119,322)(120,321)
(121,328)(122,327)(123,326)(124,325)(125,332)(126,331)(127,330)(128,329)
(129,336)(130,335)(131,334)(132,333)(133,340)(134,339)(135,338)(136,337)
(137,344)(138,343)(139,342)(140,341)(141,348)(142,347)(143,346)(144,345)
(145,352)(146,351)(147,350)(148,349)(149,356)(150,355)(151,354)(152,353)
(153,360)(154,359)(155,358)(156,357)(157,364)(158,363)(159,362)(160,361)
(161,368)(162,367)(163,366)(164,365)(165,372)(166,371)(167,370)(168,369)
(169,376)(170,375)(171,374)(172,373)(173,380)(174,379)(175,378)(176,377)
(177,384)(178,383)(179,382)(180,381)(181,388)(182,387)(183,386)(184,385)
(185,392)(186,391)(187,390)(188,389)(189,396)(190,395)(191,394)(192,393)
(193,400)(194,399)(195,398)(196,397)(197,404)(198,403)(199,402)(200,401)
(201,408)(202,407)(203,406)(204,405);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*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*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(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);
s1 := Sym(408)!( 1, 73)( 2, 74)( 3, 76)( 4, 75)( 5, 69)( 6, 70)( 7, 72)
( 8, 71)( 9,133)( 10,134)( 11,136)( 12,135)( 13,129)( 14,130)( 15,132)
( 16,131)( 17,125)( 18,126)( 19,128)( 20,127)( 21,121)( 22,122)( 23,124)
( 24,123)( 25,117)( 26,118)( 27,120)( 28,119)( 29,113)( 30,114)( 31,116)
( 32,115)( 33,109)( 34,110)( 35,112)( 36,111)( 37,105)( 38,106)( 39,108)
( 40,107)( 41,101)( 42,102)( 43,104)( 44,103)( 45, 97)( 46, 98)( 47,100)
( 48, 99)( 49, 93)( 50, 94)( 51, 96)( 52, 95)( 53, 89)( 54, 90)( 55, 92)
( 56, 91)( 57, 85)( 58, 86)( 59, 88)( 60, 87)( 61, 81)( 62, 82)( 63, 84)
( 64, 83)( 65, 77)( 66, 78)( 67, 80)( 68, 79)(137,141)(138,142)(139,144)
(140,143)(145,201)(146,202)(147,204)(148,203)(149,197)(150,198)(151,200)
(152,199)(153,193)(154,194)(155,196)(156,195)(157,189)(158,190)(159,192)
(160,191)(161,185)(162,186)(163,188)(164,187)(165,181)(166,182)(167,184)
(168,183)(169,177)(170,178)(171,180)(172,179)(175,176)(205,277)(206,278)
(207,280)(208,279)(209,273)(210,274)(211,276)(212,275)(213,337)(214,338)
(215,340)(216,339)(217,333)(218,334)(219,336)(220,335)(221,329)(222,330)
(223,332)(224,331)(225,325)(226,326)(227,328)(228,327)(229,321)(230,322)
(231,324)(232,323)(233,317)(234,318)(235,320)(236,319)(237,313)(238,314)
(239,316)(240,315)(241,309)(242,310)(243,312)(244,311)(245,305)(246,306)
(247,308)(248,307)(249,301)(250,302)(251,304)(252,303)(253,297)(254,298)
(255,300)(256,299)(257,293)(258,294)(259,296)(260,295)(261,289)(262,290)
(263,292)(264,291)(265,285)(266,286)(267,288)(268,287)(269,281)(270,282)
(271,284)(272,283)(341,345)(342,346)(343,348)(344,347)(349,405)(350,406)
(351,408)(352,407)(353,401)(354,402)(355,404)(356,403)(357,397)(358,398)
(359,400)(360,399)(361,393)(362,394)(363,396)(364,395)(365,389)(366,390)
(367,392)(368,391)(369,385)(370,386)(371,388)(372,387)(373,381)(374,382)
(375,384)(376,383)(379,380);
s2 := Sym(408)!( 1,208)( 2,207)( 3,206)( 4,205)( 5,212)( 6,211)( 7,210)
( 8,209)( 9,216)( 10,215)( 11,214)( 12,213)( 13,220)( 14,219)( 15,218)
( 16,217)( 17,224)( 18,223)( 19,222)( 20,221)( 21,228)( 22,227)( 23,226)
( 24,225)( 25,232)( 26,231)( 27,230)( 28,229)( 29,236)( 30,235)( 31,234)
( 32,233)( 33,240)( 34,239)( 35,238)( 36,237)( 37,244)( 38,243)( 39,242)
( 40,241)( 41,248)( 42,247)( 43,246)( 44,245)( 45,252)( 46,251)( 47,250)
( 48,249)( 49,256)( 50,255)( 51,254)( 52,253)( 53,260)( 54,259)( 55,258)
( 56,257)( 57,264)( 58,263)( 59,262)( 60,261)( 61,268)( 62,267)( 63,266)
( 64,265)( 65,272)( 66,271)( 67,270)( 68,269)( 69,276)( 70,275)( 71,274)
( 72,273)( 73,280)( 74,279)( 75,278)( 76,277)( 77,284)( 78,283)( 79,282)
( 80,281)( 81,288)( 82,287)( 83,286)( 84,285)( 85,292)( 86,291)( 87,290)
( 88,289)( 89,296)( 90,295)( 91,294)( 92,293)( 93,300)( 94,299)( 95,298)
( 96,297)( 97,304)( 98,303)( 99,302)(100,301)(101,308)(102,307)(103,306)
(104,305)(105,312)(106,311)(107,310)(108,309)(109,316)(110,315)(111,314)
(112,313)(113,320)(114,319)(115,318)(116,317)(117,324)(118,323)(119,322)
(120,321)(121,328)(122,327)(123,326)(124,325)(125,332)(126,331)(127,330)
(128,329)(129,336)(130,335)(131,334)(132,333)(133,340)(134,339)(135,338)
(136,337)(137,344)(138,343)(139,342)(140,341)(141,348)(142,347)(143,346)
(144,345)(145,352)(146,351)(147,350)(148,349)(149,356)(150,355)(151,354)
(152,353)(153,360)(154,359)(155,358)(156,357)(157,364)(158,363)(159,362)
(160,361)(161,368)(162,367)(163,366)(164,365)(165,372)(166,371)(167,370)
(168,369)(169,376)(170,375)(171,374)(172,373)(173,380)(174,379)(175,378)
(176,377)(177,384)(178,383)(179,382)(180,381)(181,388)(182,387)(183,386)
(184,385)(185,392)(186,391)(187,390)(188,389)(189,396)(190,395)(191,394)
(192,393)(193,400)(194,399)(195,398)(196,397)(197,404)(198,403)(199,402)
(200,401)(201,408)(202,407)(203,406)(204,405);
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*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*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