Polytope of Type {2,4,102}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,102}*1632b
if this polytope has a name.
Group : SmallGroup(1632,1200)
Rank : 4
Schlafli Type : {2,4,102}
Number of vertices, edges, etc : 2, 4, 204, 102
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 : {2,4,51}*816
   17-fold quotients : {2,4,6}*96c
   34-fold quotients : {2,4,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  3,  5)(  4,  6)(  7,  9)(  8, 10)( 11, 13)( 12, 14)( 15, 17)( 16, 18)
( 19, 21)( 20, 22)( 23, 25)( 24, 26)( 27, 29)( 28, 30)( 31, 33)( 32, 34)
( 35, 37)( 36, 38)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)( 48, 50)
( 51, 53)( 52, 54)( 55, 57)( 56, 58)( 59, 61)( 60, 62)( 63, 65)( 64, 66)
( 67, 69)( 68, 70)( 71, 73)( 72, 74)( 75, 77)( 76, 78)( 79, 81)( 80, 82)
( 83, 85)( 84, 86)( 87, 89)( 88, 90)( 91, 93)( 92, 94)( 95, 97)( 96, 98)
( 99,101)(100,102)(103,105)(104,106)(107,109)(108,110)(111,113)(112,114)
(115,117)(116,118)(119,121)(120,122)(123,125)(124,126)(127,129)(128,130)
(131,133)(132,134)(135,137)(136,138)(139,141)(140,142)(143,145)(144,146)
(147,149)(148,150)(151,153)(152,154)(155,157)(156,158)(159,161)(160,162)
(163,165)(164,166)(167,169)(168,170)(171,173)(172,174)(175,177)(176,178)
(179,181)(180,182)(183,185)(184,186)(187,189)(188,190)(191,193)(192,194)
(195,197)(196,198)(199,201)(200,202)(203,205)(204,206)(207,209)(208,210)
(211,213)(212,214)(215,217)(216,218)(219,221)(220,222)(223,225)(224,226)
(227,229)(228,230)(231,233)(232,234)(235,237)(236,238)(239,241)(240,242)
(243,245)(244,246)(247,249)(248,250)(251,253)(252,254)(255,257)(256,258)
(259,261)(260,262)(263,265)(264,266)(267,269)(268,270)(271,273)(272,274)
(275,277)(276,278)(279,281)(280,282)(283,285)(284,286)(287,289)(288,290)
(291,293)(292,294)(295,297)(296,298)(299,301)(300,302)(303,305)(304,306)
(307,309)(308,310)(311,313)(312,314)(315,317)(316,318)(319,321)(320,322)
(323,325)(324,326)(327,329)(328,330)(331,333)(332,334)(335,337)(336,338)
(339,341)(340,342)(343,345)(344,346)(347,349)(348,350)(351,353)(352,354)
(355,357)(356,358)(359,361)(360,362)(363,365)(364,366)(367,369)(368,370)
(371,373)(372,374)(375,377)(376,378)(379,381)(380,382)(383,385)(384,386)
(387,389)(388,390)(391,393)(392,394)(395,397)(396,398)(399,401)(400,402)
(403,405)(404,406)(407,409)(408,410);;
s2 := (  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);;
s3 := (  3,347)(  4,350)(  5,349)(  6,348)(  7,343)(  8,346)(  9,345)( 10,344)
( 11,407)( 12,410)( 13,409)( 14,408)( 15,403)( 16,406)( 17,405)( 18,404)
( 19,399)( 20,402)( 21,401)( 22,400)( 23,395)( 24,398)( 25,397)( 26,396)
( 27,391)( 28,394)( 29,393)( 30,392)( 31,387)( 32,390)( 33,389)( 34,388)
( 35,383)( 36,386)( 37,385)( 38,384)( 39,379)( 40,382)( 41,381)( 42,380)
( 43,375)( 44,378)( 45,377)( 46,376)( 47,371)( 48,374)( 49,373)( 50,372)
( 51,367)( 52,370)( 53,369)( 54,368)( 55,363)( 56,366)( 57,365)( 58,364)
( 59,359)( 60,362)( 61,361)( 62,360)( 63,355)( 64,358)( 65,357)( 66,356)
( 67,351)( 68,354)( 69,353)( 70,352)( 71,279)( 72,282)( 73,281)( 74,280)
( 75,275)( 76,278)( 77,277)( 78,276)( 79,339)( 80,342)( 81,341)( 82,340)
( 83,335)( 84,338)( 85,337)( 86,336)( 87,331)( 88,334)( 89,333)( 90,332)
( 91,327)( 92,330)( 93,329)( 94,328)( 95,323)( 96,326)( 97,325)( 98,324)
( 99,319)(100,322)(101,321)(102,320)(103,315)(104,318)(105,317)(106,316)
(107,311)(108,314)(109,313)(110,312)(111,307)(112,310)(113,309)(114,308)
(115,303)(116,306)(117,305)(118,304)(119,299)(120,302)(121,301)(122,300)
(123,295)(124,298)(125,297)(126,296)(127,291)(128,294)(129,293)(130,292)
(131,287)(132,290)(133,289)(134,288)(135,283)(136,286)(137,285)(138,284)
(139,211)(140,214)(141,213)(142,212)(143,207)(144,210)(145,209)(146,208)
(147,271)(148,274)(149,273)(150,272)(151,267)(152,270)(153,269)(154,268)
(155,263)(156,266)(157,265)(158,264)(159,259)(160,262)(161,261)(162,260)
(163,255)(164,258)(165,257)(166,256)(167,251)(168,254)(169,253)(170,252)
(171,247)(172,250)(173,249)(174,248)(175,243)(176,246)(177,245)(178,244)
(179,239)(180,242)(181,241)(182,240)(183,235)(184,238)(185,237)(186,236)
(187,231)(188,234)(189,233)(190,232)(191,227)(192,230)(193,229)(194,228)
(195,223)(196,226)(197,225)(198,224)(199,219)(200,222)(201,221)(202,220)
(203,215)(204,218)(205,217)(206,216);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(410)!(1,2);
s1 := Sym(410)!(  3,  5)(  4,  6)(  7,  9)(  8, 10)( 11, 13)( 12, 14)( 15, 17)
( 16, 18)( 19, 21)( 20, 22)( 23, 25)( 24, 26)( 27, 29)( 28, 30)( 31, 33)
( 32, 34)( 35, 37)( 36, 38)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)
( 48, 50)( 51, 53)( 52, 54)( 55, 57)( 56, 58)( 59, 61)( 60, 62)( 63, 65)
( 64, 66)( 67, 69)( 68, 70)( 71, 73)( 72, 74)( 75, 77)( 76, 78)( 79, 81)
( 80, 82)( 83, 85)( 84, 86)( 87, 89)( 88, 90)( 91, 93)( 92, 94)( 95, 97)
( 96, 98)( 99,101)(100,102)(103,105)(104,106)(107,109)(108,110)(111,113)
(112,114)(115,117)(116,118)(119,121)(120,122)(123,125)(124,126)(127,129)
(128,130)(131,133)(132,134)(135,137)(136,138)(139,141)(140,142)(143,145)
(144,146)(147,149)(148,150)(151,153)(152,154)(155,157)(156,158)(159,161)
(160,162)(163,165)(164,166)(167,169)(168,170)(171,173)(172,174)(175,177)
(176,178)(179,181)(180,182)(183,185)(184,186)(187,189)(188,190)(191,193)
(192,194)(195,197)(196,198)(199,201)(200,202)(203,205)(204,206)(207,209)
(208,210)(211,213)(212,214)(215,217)(216,218)(219,221)(220,222)(223,225)
(224,226)(227,229)(228,230)(231,233)(232,234)(235,237)(236,238)(239,241)
(240,242)(243,245)(244,246)(247,249)(248,250)(251,253)(252,254)(255,257)
(256,258)(259,261)(260,262)(263,265)(264,266)(267,269)(268,270)(271,273)
(272,274)(275,277)(276,278)(279,281)(280,282)(283,285)(284,286)(287,289)
(288,290)(291,293)(292,294)(295,297)(296,298)(299,301)(300,302)(303,305)
(304,306)(307,309)(308,310)(311,313)(312,314)(315,317)(316,318)(319,321)
(320,322)(323,325)(324,326)(327,329)(328,330)(331,333)(332,334)(335,337)
(336,338)(339,341)(340,342)(343,345)(344,346)(347,349)(348,350)(351,353)
(352,354)(355,357)(356,358)(359,361)(360,362)(363,365)(364,366)(367,369)
(368,370)(371,373)(372,374)(375,377)(376,378)(379,381)(380,382)(383,385)
(384,386)(387,389)(388,390)(391,393)(392,394)(395,397)(396,398)(399,401)
(400,402)(403,405)(404,406)(407,409)(408,410);
s2 := 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);
s3 := Sym(410)!(  3,347)(  4,350)(  5,349)(  6,348)(  7,343)(  8,346)(  9,345)
( 10,344)( 11,407)( 12,410)( 13,409)( 14,408)( 15,403)( 16,406)( 17,405)
( 18,404)( 19,399)( 20,402)( 21,401)( 22,400)( 23,395)( 24,398)( 25,397)
( 26,396)( 27,391)( 28,394)( 29,393)( 30,392)( 31,387)( 32,390)( 33,389)
( 34,388)( 35,383)( 36,386)( 37,385)( 38,384)( 39,379)( 40,382)( 41,381)
( 42,380)( 43,375)( 44,378)( 45,377)( 46,376)( 47,371)( 48,374)( 49,373)
( 50,372)( 51,367)( 52,370)( 53,369)( 54,368)( 55,363)( 56,366)( 57,365)
( 58,364)( 59,359)( 60,362)( 61,361)( 62,360)( 63,355)( 64,358)( 65,357)
( 66,356)( 67,351)( 68,354)( 69,353)( 70,352)( 71,279)( 72,282)( 73,281)
( 74,280)( 75,275)( 76,278)( 77,277)( 78,276)( 79,339)( 80,342)( 81,341)
( 82,340)( 83,335)( 84,338)( 85,337)( 86,336)( 87,331)( 88,334)( 89,333)
( 90,332)( 91,327)( 92,330)( 93,329)( 94,328)( 95,323)( 96,326)( 97,325)
( 98,324)( 99,319)(100,322)(101,321)(102,320)(103,315)(104,318)(105,317)
(106,316)(107,311)(108,314)(109,313)(110,312)(111,307)(112,310)(113,309)
(114,308)(115,303)(116,306)(117,305)(118,304)(119,299)(120,302)(121,301)
(122,300)(123,295)(124,298)(125,297)(126,296)(127,291)(128,294)(129,293)
(130,292)(131,287)(132,290)(133,289)(134,288)(135,283)(136,286)(137,285)
(138,284)(139,211)(140,214)(141,213)(142,212)(143,207)(144,210)(145,209)
(146,208)(147,271)(148,274)(149,273)(150,272)(151,267)(152,270)(153,269)
(154,268)(155,263)(156,266)(157,265)(158,264)(159,259)(160,262)(161,261)
(162,260)(163,255)(164,258)(165,257)(166,256)(167,251)(168,254)(169,253)
(170,252)(171,247)(172,250)(173,249)(174,248)(175,243)(176,246)(177,245)
(178,244)(179,239)(180,242)(181,241)(182,240)(183,235)(184,238)(185,237)
(186,236)(187,231)(188,234)(189,233)(190,232)(191,227)(192,230)(193,229)
(194,228)(195,223)(196,226)(197,225)(198,224)(199,219)(200,222)(201,221)
(202,220)(203,215)(204,218)(205,217)(206,216);
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope