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Polytope of Type {2,102,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,102,4}*1632c
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}*96b
   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 := (  3,210)(  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*s3*s2*s1*s3*s2*s1*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 ];;
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)!(  3,210)(  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*s3*s2*s1*s3*s2*s1*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 >; 
 

to this polytope