Polytope of Type {2,51,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,51,4}*1632
if this polytope has a name.
Group : SmallGroup(1632,1200)
Rank : 4
Schlafli Type : {2,51,4}
Number of vertices, edges, etc : 2, 102, 204, 8
Order of s0s1s2s3 : 102
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
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) :
2-fold quotients : {2,51,4}*816
4-fold quotients : {2,51,2}*408
12-fold quotients : {2,17,2}*136
17-fold quotients : {2,3,4}*96
34-fold quotients : {2,3,4}*48
68-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 7, 67)( 8, 69)( 9, 68)( 10, 70)( 11, 63)( 12, 65)( 13, 64)
( 14, 66)( 15, 59)( 16, 61)( 17, 60)( 18, 62)( 19, 55)( 20, 57)( 21, 56)
( 22, 58)( 23, 51)( 24, 53)( 25, 52)( 26, 54)( 27, 47)( 28, 49)( 29, 48)
( 30, 50)( 31, 43)( 32, 45)( 33, 44)( 34, 46)( 35, 39)( 36, 41)( 37, 40)
( 38, 42)( 71,139)( 72,141)( 73,140)( 74,142)( 75,203)( 76,205)( 77,204)
( 78,206)( 79,199)( 80,201)( 81,200)( 82,202)( 83,195)( 84,197)( 85,196)
( 86,198)( 87,191)( 88,193)( 89,192)( 90,194)( 91,187)( 92,189)( 93,188)
( 94,190)( 95,183)( 96,185)( 97,184)( 98,186)( 99,179)(100,181)(101,180)
(102,182)(103,175)(104,177)(105,176)(106,178)(107,171)(108,173)(109,172)
(110,174)(111,167)(112,169)(113,168)(114,170)(115,163)(116,165)(117,164)
(118,166)(119,159)(120,161)(121,160)(122,162)(123,155)(124,157)(125,156)
(126,158)(127,151)(128,153)(129,152)(130,154)(131,147)(132,149)(133,148)
(134,150)(135,143)(136,145)(137,144)(138,146)(208,209)(211,271)(212,273)
(213,272)(214,274)(215,267)(216,269)(217,268)(218,270)(219,263)(220,265)
(221,264)(222,266)(223,259)(224,261)(225,260)(226,262)(227,255)(228,257)
(229,256)(230,258)(231,251)(232,253)(233,252)(234,254)(235,247)(236,249)
(237,248)(238,250)(239,243)(240,245)(241,244)(242,246)(275,343)(276,345)
(277,344)(278,346)(279,407)(280,409)(281,408)(282,410)(283,403)(284,405)
(285,404)(286,406)(287,399)(288,401)(289,400)(290,402)(291,395)(292,397)
(293,396)(294,398)(295,391)(296,393)(297,392)(298,394)(299,387)(300,389)
(301,388)(302,390)(303,383)(304,385)(305,384)(306,386)(307,379)(308,381)
(309,380)(310,382)(311,375)(312,377)(313,376)(314,378)(315,371)(316,373)
(317,372)(318,374)(319,367)(320,369)(321,368)(322,370)(323,363)(324,365)
(325,364)(326,366)(327,359)(328,361)(329,360)(330,362)(331,355)(332,357)
(333,356)(334,358)(335,351)(336,353)(337,352)(338,354)(339,347)(340,349)
(341,348)(342,350);;
s2 := ( 3, 75)( 4, 76)( 5, 78)( 6, 77)( 7, 71)( 8, 72)( 9, 74)( 10, 73)
( 11,135)( 12,136)( 13,138)( 14,137)( 15,131)( 16,132)( 17,134)( 18,133)
( 19,127)( 20,128)( 21,130)( 22,129)( 23,123)( 24,124)( 25,126)( 26,125)
( 27,119)( 28,120)( 29,122)( 30,121)( 31,115)( 32,116)( 33,118)( 34,117)
( 35,111)( 36,112)( 37,114)( 38,113)( 39,107)( 40,108)( 41,110)( 42,109)
( 43,103)( 44,104)( 45,106)( 46,105)( 47, 99)( 48,100)( 49,102)( 50,101)
( 51, 95)( 52, 96)( 53, 98)( 54, 97)( 55, 91)( 56, 92)( 57, 94)( 58, 93)
( 59, 87)( 60, 88)( 61, 90)( 62, 89)( 63, 83)( 64, 84)( 65, 86)( 66, 85)
( 67, 79)( 68, 80)( 69, 82)( 70, 81)(139,143)(140,144)(141,146)(142,145)
(147,203)(148,204)(149,206)(150,205)(151,199)(152,200)(153,202)(154,201)
(155,195)(156,196)(157,198)(158,197)(159,191)(160,192)(161,194)(162,193)
(163,187)(164,188)(165,190)(166,189)(167,183)(168,184)(169,186)(170,185)
(171,179)(172,180)(173,182)(174,181)(177,178)(207,279)(208,280)(209,282)
(210,281)(211,275)(212,276)(213,278)(214,277)(215,339)(216,340)(217,342)
(218,341)(219,335)(220,336)(221,338)(222,337)(223,331)(224,332)(225,334)
(226,333)(227,327)(228,328)(229,330)(230,329)(231,323)(232,324)(233,326)
(234,325)(235,319)(236,320)(237,322)(238,321)(239,315)(240,316)(241,318)
(242,317)(243,311)(244,312)(245,314)(246,313)(247,307)(248,308)(249,310)
(250,309)(251,303)(252,304)(253,306)(254,305)(255,299)(256,300)(257,302)
(258,301)(259,295)(260,296)(261,298)(262,297)(263,291)(264,292)(265,294)
(266,293)(267,287)(268,288)(269,290)(270,289)(271,283)(272,284)(273,286)
(274,285)(343,347)(344,348)(345,350)(346,349)(351,407)(352,408)(353,410)
(354,409)(355,403)(356,404)(357,406)(358,405)(359,399)(360,400)(361,402)
(362,401)(363,395)(364,396)(365,398)(366,397)(367,391)(368,392)(369,394)
(370,393)(371,387)(372,388)(373,390)(374,389)(375,383)(376,384)(377,386)
(378,385)(381,382);;
s3 := ( 3,210)( 4,209)( 5,208)( 6,207)( 7,214)( 8,213)( 9,212)( 10,211)
( 11,218)( 12,217)( 13,216)( 14,215)( 15,222)( 16,221)( 17,220)( 18,219)
( 19,226)( 20,225)( 21,224)( 22,223)( 23,230)( 24,229)( 25,228)( 26,227)
( 27,234)( 28,233)( 29,232)( 30,231)( 31,238)( 32,237)( 33,236)( 34,235)
( 35,242)( 36,241)( 37,240)( 38,239)( 39,246)( 40,245)( 41,244)( 42,243)
( 43,250)( 44,249)( 45,248)( 46,247)( 47,254)( 48,253)( 49,252)( 50,251)
( 51,258)( 52,257)( 53,256)( 54,255)( 55,262)( 56,261)( 57,260)( 58,259)
( 59,266)( 60,265)( 61,264)( 62,263)( 63,270)( 64,269)( 65,268)( 66,267)
( 67,274)( 68,273)( 69,272)( 70,271)( 71,278)( 72,277)( 73,276)( 74,275)
( 75,282)( 76,281)( 77,280)( 78,279)( 79,286)( 80,285)( 81,284)( 82,283)
( 83,290)( 84,289)( 85,288)( 86,287)( 87,294)( 88,293)( 89,292)( 90,291)
( 91,298)( 92,297)( 93,296)( 94,295)( 95,302)( 96,301)( 97,300)( 98,299)
( 99,306)(100,305)(101,304)(102,303)(103,310)(104,309)(105,308)(106,307)
(107,314)(108,313)(109,312)(110,311)(111,318)(112,317)(113,316)(114,315)
(115,322)(116,321)(117,320)(118,319)(119,326)(120,325)(121,324)(122,323)
(123,330)(124,329)(125,328)(126,327)(127,334)(128,333)(129,332)(130,331)
(131,338)(132,337)(133,336)(134,335)(135,342)(136,341)(137,340)(138,339)
(139,346)(140,345)(141,344)(142,343)(143,350)(144,349)(145,348)(146,347)
(147,354)(148,353)(149,352)(150,351)(151,358)(152,357)(153,356)(154,355)
(155,362)(156,361)(157,360)(158,359)(159,366)(160,365)(161,364)(162,363)
(163,370)(164,369)(165,368)(166,367)(167,374)(168,373)(169,372)(170,371)
(171,378)(172,377)(173,376)(174,375)(175,382)(176,381)(177,380)(178,379)
(179,386)(180,385)(181,384)(182,383)(183,390)(184,389)(185,388)(186,387)
(187,394)(188,393)(189,392)(190,391)(191,398)(192,397)(193,396)(194,395)
(195,402)(196,401)(197,400)(198,399)(199,406)(200,405)(201,404)(202,403)
(203,410)(204,409)(205,408)(206,407);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s1*s2*s3*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(410)!(1,2);
s1 := Sym(410)!( 4, 5)( 7, 67)( 8, 69)( 9, 68)( 10, 70)( 11, 63)( 12, 65)
( 13, 64)( 14, 66)( 15, 59)( 16, 61)( 17, 60)( 18, 62)( 19, 55)( 20, 57)
( 21, 56)( 22, 58)( 23, 51)( 24, 53)( 25, 52)( 26, 54)( 27, 47)( 28, 49)
( 29, 48)( 30, 50)( 31, 43)( 32, 45)( 33, 44)( 34, 46)( 35, 39)( 36, 41)
( 37, 40)( 38, 42)( 71,139)( 72,141)( 73,140)( 74,142)( 75,203)( 76,205)
( 77,204)( 78,206)( 79,199)( 80,201)( 81,200)( 82,202)( 83,195)( 84,197)
( 85,196)( 86,198)( 87,191)( 88,193)( 89,192)( 90,194)( 91,187)( 92,189)
( 93,188)( 94,190)( 95,183)( 96,185)( 97,184)( 98,186)( 99,179)(100,181)
(101,180)(102,182)(103,175)(104,177)(105,176)(106,178)(107,171)(108,173)
(109,172)(110,174)(111,167)(112,169)(113,168)(114,170)(115,163)(116,165)
(117,164)(118,166)(119,159)(120,161)(121,160)(122,162)(123,155)(124,157)
(125,156)(126,158)(127,151)(128,153)(129,152)(130,154)(131,147)(132,149)
(133,148)(134,150)(135,143)(136,145)(137,144)(138,146)(208,209)(211,271)
(212,273)(213,272)(214,274)(215,267)(216,269)(217,268)(218,270)(219,263)
(220,265)(221,264)(222,266)(223,259)(224,261)(225,260)(226,262)(227,255)
(228,257)(229,256)(230,258)(231,251)(232,253)(233,252)(234,254)(235,247)
(236,249)(237,248)(238,250)(239,243)(240,245)(241,244)(242,246)(275,343)
(276,345)(277,344)(278,346)(279,407)(280,409)(281,408)(282,410)(283,403)
(284,405)(285,404)(286,406)(287,399)(288,401)(289,400)(290,402)(291,395)
(292,397)(293,396)(294,398)(295,391)(296,393)(297,392)(298,394)(299,387)
(300,389)(301,388)(302,390)(303,383)(304,385)(305,384)(306,386)(307,379)
(308,381)(309,380)(310,382)(311,375)(312,377)(313,376)(314,378)(315,371)
(316,373)(317,372)(318,374)(319,367)(320,369)(321,368)(322,370)(323,363)
(324,365)(325,364)(326,366)(327,359)(328,361)(329,360)(330,362)(331,355)
(332,357)(333,356)(334,358)(335,351)(336,353)(337,352)(338,354)(339,347)
(340,349)(341,348)(342,350);
s2 := Sym(410)!( 3, 75)( 4, 76)( 5, 78)( 6, 77)( 7, 71)( 8, 72)( 9, 74)
( 10, 73)( 11,135)( 12,136)( 13,138)( 14,137)( 15,131)( 16,132)( 17,134)
( 18,133)( 19,127)( 20,128)( 21,130)( 22,129)( 23,123)( 24,124)( 25,126)
( 26,125)( 27,119)( 28,120)( 29,122)( 30,121)( 31,115)( 32,116)( 33,118)
( 34,117)( 35,111)( 36,112)( 37,114)( 38,113)( 39,107)( 40,108)( 41,110)
( 42,109)( 43,103)( 44,104)( 45,106)( 46,105)( 47, 99)( 48,100)( 49,102)
( 50,101)( 51, 95)( 52, 96)( 53, 98)( 54, 97)( 55, 91)( 56, 92)( 57, 94)
( 58, 93)( 59, 87)( 60, 88)( 61, 90)( 62, 89)( 63, 83)( 64, 84)( 65, 86)
( 66, 85)( 67, 79)( 68, 80)( 69, 82)( 70, 81)(139,143)(140,144)(141,146)
(142,145)(147,203)(148,204)(149,206)(150,205)(151,199)(152,200)(153,202)
(154,201)(155,195)(156,196)(157,198)(158,197)(159,191)(160,192)(161,194)
(162,193)(163,187)(164,188)(165,190)(166,189)(167,183)(168,184)(169,186)
(170,185)(171,179)(172,180)(173,182)(174,181)(177,178)(207,279)(208,280)
(209,282)(210,281)(211,275)(212,276)(213,278)(214,277)(215,339)(216,340)
(217,342)(218,341)(219,335)(220,336)(221,338)(222,337)(223,331)(224,332)
(225,334)(226,333)(227,327)(228,328)(229,330)(230,329)(231,323)(232,324)
(233,326)(234,325)(235,319)(236,320)(237,322)(238,321)(239,315)(240,316)
(241,318)(242,317)(243,311)(244,312)(245,314)(246,313)(247,307)(248,308)
(249,310)(250,309)(251,303)(252,304)(253,306)(254,305)(255,299)(256,300)
(257,302)(258,301)(259,295)(260,296)(261,298)(262,297)(263,291)(264,292)
(265,294)(266,293)(267,287)(268,288)(269,290)(270,289)(271,283)(272,284)
(273,286)(274,285)(343,347)(344,348)(345,350)(346,349)(351,407)(352,408)
(353,410)(354,409)(355,403)(356,404)(357,406)(358,405)(359,399)(360,400)
(361,402)(362,401)(363,395)(364,396)(365,398)(366,397)(367,391)(368,392)
(369,394)(370,393)(371,387)(372,388)(373,390)(374,389)(375,383)(376,384)
(377,386)(378,385)(381,382);
s3 := Sym(410)!( 3,210)( 4,209)( 5,208)( 6,207)( 7,214)( 8,213)( 9,212)
( 10,211)( 11,218)( 12,217)( 13,216)( 14,215)( 15,222)( 16,221)( 17,220)
( 18,219)( 19,226)( 20,225)( 21,224)( 22,223)( 23,230)( 24,229)( 25,228)
( 26,227)( 27,234)( 28,233)( 29,232)( 30,231)( 31,238)( 32,237)( 33,236)
( 34,235)( 35,242)( 36,241)( 37,240)( 38,239)( 39,246)( 40,245)( 41,244)
( 42,243)( 43,250)( 44,249)( 45,248)( 46,247)( 47,254)( 48,253)( 49,252)
( 50,251)( 51,258)( 52,257)( 53,256)( 54,255)( 55,262)( 56,261)( 57,260)
( 58,259)( 59,266)( 60,265)( 61,264)( 62,263)( 63,270)( 64,269)( 65,268)
( 66,267)( 67,274)( 68,273)( 69,272)( 70,271)( 71,278)( 72,277)( 73,276)
( 74,275)( 75,282)( 76,281)( 77,280)( 78,279)( 79,286)( 80,285)( 81,284)
( 82,283)( 83,290)( 84,289)( 85,288)( 86,287)( 87,294)( 88,293)( 89,292)
( 90,291)( 91,298)( 92,297)( 93,296)( 94,295)( 95,302)( 96,301)( 97,300)
( 98,299)( 99,306)(100,305)(101,304)(102,303)(103,310)(104,309)(105,308)
(106,307)(107,314)(108,313)(109,312)(110,311)(111,318)(112,317)(113,316)
(114,315)(115,322)(116,321)(117,320)(118,319)(119,326)(120,325)(121,324)
(122,323)(123,330)(124,329)(125,328)(126,327)(127,334)(128,333)(129,332)
(130,331)(131,338)(132,337)(133,336)(134,335)(135,342)(136,341)(137,340)
(138,339)(139,346)(140,345)(141,344)(142,343)(143,350)(144,349)(145,348)
(146,347)(147,354)(148,353)(149,352)(150,351)(151,358)(152,357)(153,356)
(154,355)(155,362)(156,361)(157,360)(158,359)(159,366)(160,365)(161,364)
(162,363)(163,370)(164,369)(165,368)(166,367)(167,374)(168,373)(169,372)
(170,371)(171,378)(172,377)(173,376)(174,375)(175,382)(176,381)(177,380)
(178,379)(179,386)(180,385)(181,384)(182,383)(183,390)(184,389)(185,388)
(186,387)(187,394)(188,393)(189,392)(190,391)(191,398)(192,397)(193,396)
(194,395)(195,402)(196,401)(197,400)(198,399)(199,406)(200,405)(201,404)
(202,403)(203,410)(204,409)(205,408)(206,407);
poly := sub<Sym(410)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s1*s2*s1*s2*s3*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 >;
to this polytope