Polytope of Type {2,102,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,102,4}*1632b
if this polytope has a name.
Group : SmallGroup(1632,1200)
Rank : 4
Schlafli Type : {2,102,4}
Number of vertices, edges, etc : 2, 102, 204, 4
Order of s₀s₁s₂s₃ : 102
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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
   17-fold quotients : {2,6,4}*96c
   34-fold quotients : {2,3,4}*48
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 := (  3,279)(  4,280)(  5,282)(  6,281)(  7,275)(  8,276)(  9,278)( 10,277)
( 11,339)( 12,340)( 13,342)( 14,341)( 15,335)( 16,336)( 17,338)( 18,337)
( 19,331)( 20,332)( 21,334)( 22,333)( 23,327)( 24,328)( 25,330)( 26,329)
( 27,323)( 28,324)( 29,326)( 30,325)( 31,319)( 32,320)( 33,322)( 34,321)
( 35,315)( 36,316)( 37,318)( 38,317)( 39,311)( 40,312)( 41,314)( 42,313)
( 43,307)( 44,308)( 45,310)( 46,309)( 47,303)( 48,304)( 49,306)( 50,305)
( 51,299)( 52,300)( 53,302)( 54,301)( 55,295)( 56,296)( 57,298)( 58,297)
( 59,291)( 60,292)( 61,294)( 62,293)( 63,287)( 64,288)( 65,290)( 66,289)
( 67,283)( 68,284)( 69,286)( 70,285)( 71,211)( 72,212)( 73,214)( 74,213)
( 75,207)( 76,208)( 77,210)( 78,209)( 79,271)( 80,272)( 81,274)( 82,273)
( 83,267)( 84,268)( 85,270)( 86,269)( 87,263)( 88,264)( 89,266)( 90,265)
( 91,259)( 92,260)( 93,262)( 94,261)( 95,255)( 96,256)( 97,258)( 98,257)
( 99,251)(100,252)(101,254)(102,253)(103,247)(104,248)(105,250)(106,249)
(107,243)(108,244)(109,246)(110,245)(111,239)(112,240)(113,242)(114,241)
(115,235)(116,236)(117,238)(118,237)(119,231)(120,232)(121,234)(122,233)
(123,227)(124,228)(125,230)(126,229)(127,223)(128,224)(129,226)(130,225)
(131,219)(132,220)(133,222)(134,221)(135,215)(136,216)(137,218)(138,217)
(139,347)(140,348)(141,350)(142,349)(143,343)(144,344)(145,346)(146,345)
(147,407)(148,408)(149,410)(150,409)(151,403)(152,404)(153,406)(154,405)
(155,399)(156,400)(157,402)(158,401)(159,395)(160,396)(161,398)(162,397)
(163,391)(164,392)(165,394)(166,393)(167,387)(168,388)(169,390)(170,389)
(171,383)(172,384)(173,386)(174,385)(175,379)(176,380)(177,382)(178,381)
(179,375)(180,376)(181,378)(182,377)(183,371)(184,372)(185,374)(186,373)
(187,367)(188,368)(189,370)(190,369)(191,363)(192,364)(193,366)(194,365)
(195,359)(196,360)(197,362)(198,361)(199,355)(200,356)(201,358)(202,357)
(203,351)(204,352)(205,354)(206,353);;
s3 := (  3,  6)(  4,  5)(  7, 10)(  8,  9)( 11, 14)( 12, 13)( 15, 18)( 16, 17)
( 19, 22)( 20, 21)( 23, 26)( 24, 25)( 27, 30)( 28, 29)( 31, 34)( 32, 33)
( 35, 38)( 36, 37)( 39, 42)( 40, 41)( 43, 46)( 44, 45)( 47, 50)( 48, 49)
( 51, 54)( 52, 53)( 55, 58)( 56, 57)( 59, 62)( 60, 61)( 63, 66)( 64, 65)
( 67, 70)( 68, 69)( 71, 74)( 72, 73)( 75, 78)( 76, 77)( 79, 82)( 80, 81)
( 83, 86)( 84, 85)( 87, 90)( 88, 89)( 91, 94)( 92, 93)( 95, 98)( 96, 97)
( 99,102)(100,101)(103,106)(104,105)(107,110)(108,109)(111,114)(112,113)
(115,118)(116,117)(119,122)(120,121)(123,126)(124,125)(127,130)(128,129)
(131,134)(132,133)(135,138)(136,137)(139,142)(140,141)(143,146)(144,145)
(147,150)(148,149)(151,154)(152,153)(155,158)(156,157)(159,162)(160,161)
(163,166)(164,165)(167,170)(168,169)(171,174)(172,173)(175,178)(176,177)
(179,182)(180,181)(183,186)(184,185)(187,190)(188,189)(191,194)(192,193)
(195,198)(196,197)(199,202)(200,201)(203,206)(204,205)(207,210)(208,209)
(211,214)(212,213)(215,218)(216,217)(219,222)(220,221)(223,226)(224,225)
(227,230)(228,229)(231,234)(232,233)(235,238)(236,237)(239,242)(240,241)
(243,246)(244,245)(247,250)(248,249)(251,254)(252,253)(255,258)(256,257)
(259,262)(260,261)(263,266)(264,265)(267,270)(268,269)(271,274)(272,273)
(275,278)(276,277)(279,282)(280,281)(283,286)(284,285)(287,290)(288,289)
(291,294)(292,293)(295,298)(296,297)(299,302)(300,301)(303,306)(304,305)
(307,310)(308,309)(311,314)(312,313)(315,318)(316,317)(319,322)(320,321)
(323,326)(324,325)(327,330)(328,329)(331,334)(332,333)(335,338)(336,337)
(339,342)(340,341)(343,346)(344,345)(347,350)(348,349)(351,354)(352,353)
(355,358)(356,357)(359,362)(360,361)(363,366)(364,365)(367,370)(368,369)
(371,374)(372,373)(375,378)(376,377)(379,382)(380,381)(383,386)(384,385)
(387,390)(388,389)(391,394)(392,393)(395,398)(396,397)(399,402)(400,401)
(403,406)(404,405)(407,410)(408,409);;
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, s3*s2*s1*s3*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)!(  3,279)(  4,280)(  5,282)(  6,281)(  7,275)(  8,276)(  9,278)
( 10,277)( 11,339)( 12,340)( 13,342)( 14,341)( 15,335)( 16,336)( 17,338)
( 18,337)( 19,331)( 20,332)( 21,334)( 22,333)( 23,327)( 24,328)( 25,330)
( 26,329)( 27,323)( 28,324)( 29,326)( 30,325)( 31,319)( 32,320)( 33,322)
( 34,321)( 35,315)( 36,316)( 37,318)( 38,317)( 39,311)( 40,312)( 41,314)
( 42,313)( 43,307)( 44,308)( 45,310)( 46,309)( 47,303)( 48,304)( 49,306)
( 50,305)( 51,299)( 52,300)( 53,302)( 54,301)( 55,295)( 56,296)( 57,298)
( 58,297)( 59,291)( 60,292)( 61,294)( 62,293)( 63,287)( 64,288)( 65,290)
( 66,289)( 67,283)( 68,284)( 69,286)( 70,285)( 71,211)( 72,212)( 73,214)
( 74,213)( 75,207)( 76,208)( 77,210)( 78,209)( 79,271)( 80,272)( 81,274)
( 82,273)( 83,267)( 84,268)( 85,270)( 86,269)( 87,263)( 88,264)( 89,266)
( 90,265)( 91,259)( 92,260)( 93,262)( 94,261)( 95,255)( 96,256)( 97,258)
( 98,257)( 99,251)(100,252)(101,254)(102,253)(103,247)(104,248)(105,250)
(106,249)(107,243)(108,244)(109,246)(110,245)(111,239)(112,240)(113,242)
(114,241)(115,235)(116,236)(117,238)(118,237)(119,231)(120,232)(121,234)
(122,233)(123,227)(124,228)(125,230)(126,229)(127,223)(128,224)(129,226)
(130,225)(131,219)(132,220)(133,222)(134,221)(135,215)(136,216)(137,218)
(138,217)(139,347)(140,348)(141,350)(142,349)(143,343)(144,344)(145,346)
(146,345)(147,407)(148,408)(149,410)(150,409)(151,403)(152,404)(153,406)
(154,405)(155,399)(156,400)(157,402)(158,401)(159,395)(160,396)(161,398)
(162,397)(163,391)(164,392)(165,394)(166,393)(167,387)(168,388)(169,390)
(170,389)(171,383)(172,384)(173,386)(174,385)(175,379)(176,380)(177,382)
(178,381)(179,375)(180,376)(181,378)(182,377)(183,371)(184,372)(185,374)
(186,373)(187,367)(188,368)(189,370)(190,369)(191,363)(192,364)(193,366)
(194,365)(195,359)(196,360)(197,362)(198,361)(199,355)(200,356)(201,358)
(202,357)(203,351)(204,352)(205,354)(206,353);
s3 := Sym(410)!(  3,  6)(  4,  5)(  7, 10)(  8,  9)( 11, 14)( 12, 13)( 15, 18)
( 16, 17)( 19, 22)( 20, 21)( 23, 26)( 24, 25)( 27, 30)( 28, 29)( 31, 34)
( 32, 33)( 35, 38)( 36, 37)( 39, 42)( 40, 41)( 43, 46)( 44, 45)( 47, 50)
( 48, 49)( 51, 54)( 52, 53)( 55, 58)( 56, 57)( 59, 62)( 60, 61)( 63, 66)
( 64, 65)( 67, 70)( 68, 69)( 71, 74)( 72, 73)( 75, 78)( 76, 77)( 79, 82)
( 80, 81)( 83, 86)( 84, 85)( 87, 90)( 88, 89)( 91, 94)( 92, 93)( 95, 98)
( 96, 97)( 99,102)(100,101)(103,106)(104,105)(107,110)(108,109)(111,114)
(112,113)(115,118)(116,117)(119,122)(120,121)(123,126)(124,125)(127,130)
(128,129)(131,134)(132,133)(135,138)(136,137)(139,142)(140,141)(143,146)
(144,145)(147,150)(148,149)(151,154)(152,153)(155,158)(156,157)(159,162)
(160,161)(163,166)(164,165)(167,170)(168,169)(171,174)(172,173)(175,178)
(176,177)(179,182)(180,181)(183,186)(184,185)(187,190)(188,189)(191,194)
(192,193)(195,198)(196,197)(199,202)(200,201)(203,206)(204,205)(207,210)
(208,209)(211,214)(212,213)(215,218)(216,217)(219,222)(220,221)(223,226)
(224,225)(227,230)(228,229)(231,234)(232,233)(235,238)(236,237)(239,242)
(240,241)(243,246)(244,245)(247,250)(248,249)(251,254)(252,253)(255,258)
(256,257)(259,262)(260,261)(263,266)(264,265)(267,270)(268,269)(271,274)
(272,273)(275,278)(276,277)(279,282)(280,281)(283,286)(284,285)(287,290)
(288,289)(291,294)(292,293)(295,298)(296,297)(299,302)(300,301)(303,306)
(304,305)(307,310)(308,309)(311,314)(312,313)(315,318)(316,317)(319,322)
(320,321)(323,326)(324,325)(327,330)(328,329)(331,334)(332,333)(335,338)
(336,337)(339,342)(340,341)(343,346)(344,345)(347,350)(348,349)(351,354)
(352,353)(355,358)(356,357)(359,362)(360,361)(363,366)(364,365)(367,370)
(368,369)(371,374)(372,373)(375,378)(376,377)(379,382)(380,381)(383,386)
(384,385)(387,390)(388,389)(391,394)(392,393)(395,398)(396,397)(399,402)
(400,401)(403,406)(404,405)(407,410)(408,409);
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, 
s3*s2*s1*s3*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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