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Polytope of Type {2,10,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,8}*1600
if this polytope has a name.
Group : SmallGroup(1600,10010)
Rank : 4
Schlafli Type : {2,10,8}
Number of vertices, edges, etc : 2, 50, 200, 40
Order of s0s1s2s3 : 8
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 : {2,10,4}*800
   4-fold quotients : {2,10,4}*400
   25-fold quotients : {2,2,8}*64
   50-fold quotients : {2,2,4}*32
   100-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  3,153)(  4,157)(  5,156)(  6,155)(  7,154)(  8,173)(  9,177)( 10,176)
( 11,175)( 12,174)( 13,168)( 14,172)( 15,171)( 16,170)( 17,169)( 18,163)
( 19,167)( 20,166)( 21,165)( 22,164)( 23,158)( 24,162)( 25,161)( 26,160)
( 27,159)( 28,178)( 29,182)( 30,181)( 31,180)( 32,179)( 33,198)( 34,202)
( 35,201)( 36,200)( 37,199)( 38,193)( 39,197)( 40,196)( 41,195)( 42,194)
( 43,188)( 44,192)( 45,191)( 46,190)( 47,189)( 48,183)( 49,187)( 50,186)
( 51,185)( 52,184)( 53,128)( 54,132)( 55,131)( 56,130)( 57,129)( 58,148)
( 59,152)( 60,151)( 61,150)( 62,149)( 63,143)( 64,147)( 65,146)( 66,145)
( 67,144)( 68,138)( 69,142)( 70,141)( 71,140)( 72,139)( 73,133)( 74,137)
( 75,136)( 76,135)( 77,134)( 78,103)( 79,107)( 80,106)( 81,105)( 82,104)
( 83,123)( 84,127)( 85,126)( 86,125)( 87,124)( 88,118)( 89,122)( 90,121)
( 91,120)( 92,119)( 93,113)( 94,117)( 95,116)( 96,115)( 97,114)( 98,108)
( 99,112)(100,111)(101,110)(102,109)(203,353)(204,357)(205,356)(206,355)
(207,354)(208,373)(209,377)(210,376)(211,375)(212,374)(213,368)(214,372)
(215,371)(216,370)(217,369)(218,363)(219,367)(220,366)(221,365)(222,364)
(223,358)(224,362)(225,361)(226,360)(227,359)(228,378)(229,382)(230,381)
(231,380)(232,379)(233,398)(234,402)(235,401)(236,400)(237,399)(238,393)
(239,397)(240,396)(241,395)(242,394)(243,388)(244,392)(245,391)(246,390)
(247,389)(248,383)(249,387)(250,386)(251,385)(252,384)(253,328)(254,332)
(255,331)(256,330)(257,329)(258,348)(259,352)(260,351)(261,350)(262,349)
(263,343)(264,347)(265,346)(266,345)(267,344)(268,338)(269,342)(270,341)
(271,340)(272,339)(273,333)(274,337)(275,336)(276,335)(277,334)(278,303)
(279,307)(280,306)(281,305)(282,304)(283,323)(284,327)(285,326)(286,325)
(287,324)(288,318)(289,322)(290,321)(291,320)(292,319)(293,313)(294,317)
(295,316)(296,315)(297,314)(298,308)(299,312)(300,311)(301,310)(302,309);;
s2 := (  3,  8)(  4, 14)(  5, 20)(  6, 26)( 10, 15)( 11, 21)( 12, 27)( 13, 23)
( 17, 22)( 19, 24)( 28, 33)( 29, 39)( 30, 45)( 31, 51)( 35, 40)( 36, 46)
( 37, 52)( 38, 48)( 42, 47)( 44, 49)( 53, 83)( 54, 89)( 55, 95)( 56,101)
( 57, 82)( 58, 78)( 59, 84)( 60, 90)( 61, 96)( 62,102)( 63, 98)( 64, 79)
( 65, 85)( 66, 91)( 67, 97)( 68, 93)( 69, 99)( 70, 80)( 71, 86)( 72, 92)
( 73, 88)( 74, 94)( 75,100)( 76, 81)( 77, 87)(103,133)(104,139)(105,145)
(106,151)(107,132)(108,128)(109,134)(110,140)(111,146)(112,152)(113,148)
(114,129)(115,135)(116,141)(117,147)(118,143)(119,149)(120,130)(121,136)
(122,142)(123,138)(124,144)(125,150)(126,131)(127,137)(153,158)(154,164)
(155,170)(156,176)(160,165)(161,171)(162,177)(163,173)(167,172)(169,174)
(178,183)(179,189)(180,195)(181,201)(185,190)(186,196)(187,202)(188,198)
(192,197)(194,199)(203,258)(204,264)(205,270)(206,276)(207,257)(208,253)
(209,259)(210,265)(211,271)(212,277)(213,273)(214,254)(215,260)(216,266)
(217,272)(218,268)(219,274)(220,255)(221,261)(222,267)(223,263)(224,269)
(225,275)(226,256)(227,262)(228,283)(229,289)(230,295)(231,301)(232,282)
(233,278)(234,284)(235,290)(236,296)(237,302)(238,298)(239,279)(240,285)
(241,291)(242,297)(243,293)(244,299)(245,280)(246,286)(247,292)(248,288)
(249,294)(250,300)(251,281)(252,287)(303,383)(304,389)(305,395)(306,401)
(307,382)(308,378)(309,384)(310,390)(311,396)(312,402)(313,398)(314,379)
(315,385)(316,391)(317,397)(318,393)(319,399)(320,380)(321,386)(322,392)
(323,388)(324,394)(325,400)(326,381)(327,387)(328,358)(329,364)(330,370)
(331,376)(332,357)(333,353)(334,359)(335,365)(336,371)(337,377)(338,373)
(339,354)(340,360)(341,366)(342,372)(343,368)(344,374)(345,355)(346,361)
(347,367)(348,363)(349,369)(350,375)(351,356)(352,362);;
s3 := (  3,203)(  4,221)(  5,209)(  6,227)(  7,215)(  8,217)(  9,205)( 10,218)
( 11,211)( 12,224)( 13,226)( 14,214)( 15,207)( 16,220)( 17,208)( 18,210)
( 19,223)( 20,216)( 21,204)( 22,222)( 23,219)( 24,212)( 25,225)( 26,213)
( 27,206)( 28,228)( 29,246)( 30,234)( 31,252)( 32,240)( 33,242)( 34,230)
( 35,243)( 36,236)( 37,249)( 38,251)( 39,239)( 40,232)( 41,245)( 42,233)
( 43,235)( 44,248)( 45,241)( 46,229)( 47,247)( 48,244)( 49,237)( 50,250)
( 51,238)( 52,231)( 53,278)( 54,296)( 55,284)( 56,302)( 57,290)( 58,292)
( 59,280)( 60,293)( 61,286)( 62,299)( 63,301)( 64,289)( 65,282)( 66,295)
( 67,283)( 68,285)( 69,298)( 70,291)( 71,279)( 72,297)( 73,294)( 74,287)
( 75,300)( 76,288)( 77,281)( 78,253)( 79,271)( 80,259)( 81,277)( 82,265)
( 83,267)( 84,255)( 85,268)( 86,261)( 87,274)( 88,276)( 89,264)( 90,257)
( 91,270)( 92,258)( 93,260)( 94,273)( 95,266)( 96,254)( 97,272)( 98,269)
( 99,262)(100,275)(101,263)(102,256)(103,328)(104,346)(105,334)(106,352)
(107,340)(108,342)(109,330)(110,343)(111,336)(112,349)(113,351)(114,339)
(115,332)(116,345)(117,333)(118,335)(119,348)(120,341)(121,329)(122,347)
(123,344)(124,337)(125,350)(126,338)(127,331)(128,303)(129,321)(130,309)
(131,327)(132,315)(133,317)(134,305)(135,318)(136,311)(137,324)(138,326)
(139,314)(140,307)(141,320)(142,308)(143,310)(144,323)(145,316)(146,304)
(147,322)(148,319)(149,312)(150,325)(151,313)(152,306)(153,353)(154,371)
(155,359)(156,377)(157,365)(158,367)(159,355)(160,368)(161,361)(162,374)
(163,376)(164,364)(165,357)(166,370)(167,358)(168,360)(169,373)(170,366)
(171,354)(172,372)(173,369)(174,362)(175,375)(176,363)(177,356)(178,378)
(179,396)(180,384)(181,402)(182,390)(183,392)(184,380)(185,393)(186,386)
(187,399)(188,401)(189,389)(190,382)(191,395)(192,383)(193,385)(194,398)
(195,391)(196,379)(197,397)(198,394)(199,387)(200,400)(201,388)(202,381);;
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, 
s3*s1*s2*s3*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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(402)!(1,2);
s1 := Sym(402)!(  3,153)(  4,157)(  5,156)(  6,155)(  7,154)(  8,173)(  9,177)
( 10,176)( 11,175)( 12,174)( 13,168)( 14,172)( 15,171)( 16,170)( 17,169)
( 18,163)( 19,167)( 20,166)( 21,165)( 22,164)( 23,158)( 24,162)( 25,161)
( 26,160)( 27,159)( 28,178)( 29,182)( 30,181)( 31,180)( 32,179)( 33,198)
( 34,202)( 35,201)( 36,200)( 37,199)( 38,193)( 39,197)( 40,196)( 41,195)
( 42,194)( 43,188)( 44,192)( 45,191)( 46,190)( 47,189)( 48,183)( 49,187)
( 50,186)( 51,185)( 52,184)( 53,128)( 54,132)( 55,131)( 56,130)( 57,129)
( 58,148)( 59,152)( 60,151)( 61,150)( 62,149)( 63,143)( 64,147)( 65,146)
( 66,145)( 67,144)( 68,138)( 69,142)( 70,141)( 71,140)( 72,139)( 73,133)
( 74,137)( 75,136)( 76,135)( 77,134)( 78,103)( 79,107)( 80,106)( 81,105)
( 82,104)( 83,123)( 84,127)( 85,126)( 86,125)( 87,124)( 88,118)( 89,122)
( 90,121)( 91,120)( 92,119)( 93,113)( 94,117)( 95,116)( 96,115)( 97,114)
( 98,108)( 99,112)(100,111)(101,110)(102,109)(203,353)(204,357)(205,356)
(206,355)(207,354)(208,373)(209,377)(210,376)(211,375)(212,374)(213,368)
(214,372)(215,371)(216,370)(217,369)(218,363)(219,367)(220,366)(221,365)
(222,364)(223,358)(224,362)(225,361)(226,360)(227,359)(228,378)(229,382)
(230,381)(231,380)(232,379)(233,398)(234,402)(235,401)(236,400)(237,399)
(238,393)(239,397)(240,396)(241,395)(242,394)(243,388)(244,392)(245,391)
(246,390)(247,389)(248,383)(249,387)(250,386)(251,385)(252,384)(253,328)
(254,332)(255,331)(256,330)(257,329)(258,348)(259,352)(260,351)(261,350)
(262,349)(263,343)(264,347)(265,346)(266,345)(267,344)(268,338)(269,342)
(270,341)(271,340)(272,339)(273,333)(274,337)(275,336)(276,335)(277,334)
(278,303)(279,307)(280,306)(281,305)(282,304)(283,323)(284,327)(285,326)
(286,325)(287,324)(288,318)(289,322)(290,321)(291,320)(292,319)(293,313)
(294,317)(295,316)(296,315)(297,314)(298,308)(299,312)(300,311)(301,310)
(302,309);
s2 := Sym(402)!(  3,  8)(  4, 14)(  5, 20)(  6, 26)( 10, 15)( 11, 21)( 12, 27)
( 13, 23)( 17, 22)( 19, 24)( 28, 33)( 29, 39)( 30, 45)( 31, 51)( 35, 40)
( 36, 46)( 37, 52)( 38, 48)( 42, 47)( 44, 49)( 53, 83)( 54, 89)( 55, 95)
( 56,101)( 57, 82)( 58, 78)( 59, 84)( 60, 90)( 61, 96)( 62,102)( 63, 98)
( 64, 79)( 65, 85)( 66, 91)( 67, 97)( 68, 93)( 69, 99)( 70, 80)( 71, 86)
( 72, 92)( 73, 88)( 74, 94)( 75,100)( 76, 81)( 77, 87)(103,133)(104,139)
(105,145)(106,151)(107,132)(108,128)(109,134)(110,140)(111,146)(112,152)
(113,148)(114,129)(115,135)(116,141)(117,147)(118,143)(119,149)(120,130)
(121,136)(122,142)(123,138)(124,144)(125,150)(126,131)(127,137)(153,158)
(154,164)(155,170)(156,176)(160,165)(161,171)(162,177)(163,173)(167,172)
(169,174)(178,183)(179,189)(180,195)(181,201)(185,190)(186,196)(187,202)
(188,198)(192,197)(194,199)(203,258)(204,264)(205,270)(206,276)(207,257)
(208,253)(209,259)(210,265)(211,271)(212,277)(213,273)(214,254)(215,260)
(216,266)(217,272)(218,268)(219,274)(220,255)(221,261)(222,267)(223,263)
(224,269)(225,275)(226,256)(227,262)(228,283)(229,289)(230,295)(231,301)
(232,282)(233,278)(234,284)(235,290)(236,296)(237,302)(238,298)(239,279)
(240,285)(241,291)(242,297)(243,293)(244,299)(245,280)(246,286)(247,292)
(248,288)(249,294)(250,300)(251,281)(252,287)(303,383)(304,389)(305,395)
(306,401)(307,382)(308,378)(309,384)(310,390)(311,396)(312,402)(313,398)
(314,379)(315,385)(316,391)(317,397)(318,393)(319,399)(320,380)(321,386)
(322,392)(323,388)(324,394)(325,400)(326,381)(327,387)(328,358)(329,364)
(330,370)(331,376)(332,357)(333,353)(334,359)(335,365)(336,371)(337,377)
(338,373)(339,354)(340,360)(341,366)(342,372)(343,368)(344,374)(345,355)
(346,361)(347,367)(348,363)(349,369)(350,375)(351,356)(352,362);
s3 := Sym(402)!(  3,203)(  4,221)(  5,209)(  6,227)(  7,215)(  8,217)(  9,205)
( 10,218)( 11,211)( 12,224)( 13,226)( 14,214)( 15,207)( 16,220)( 17,208)
( 18,210)( 19,223)( 20,216)( 21,204)( 22,222)( 23,219)( 24,212)( 25,225)
( 26,213)( 27,206)( 28,228)( 29,246)( 30,234)( 31,252)( 32,240)( 33,242)
( 34,230)( 35,243)( 36,236)( 37,249)( 38,251)( 39,239)( 40,232)( 41,245)
( 42,233)( 43,235)( 44,248)( 45,241)( 46,229)( 47,247)( 48,244)( 49,237)
( 50,250)( 51,238)( 52,231)( 53,278)( 54,296)( 55,284)( 56,302)( 57,290)
( 58,292)( 59,280)( 60,293)( 61,286)( 62,299)( 63,301)( 64,289)( 65,282)
( 66,295)( 67,283)( 68,285)( 69,298)( 70,291)( 71,279)( 72,297)( 73,294)
( 74,287)( 75,300)( 76,288)( 77,281)( 78,253)( 79,271)( 80,259)( 81,277)
( 82,265)( 83,267)( 84,255)( 85,268)( 86,261)( 87,274)( 88,276)( 89,264)
( 90,257)( 91,270)( 92,258)( 93,260)( 94,273)( 95,266)( 96,254)( 97,272)
( 98,269)( 99,262)(100,275)(101,263)(102,256)(103,328)(104,346)(105,334)
(106,352)(107,340)(108,342)(109,330)(110,343)(111,336)(112,349)(113,351)
(114,339)(115,332)(116,345)(117,333)(118,335)(119,348)(120,341)(121,329)
(122,347)(123,344)(124,337)(125,350)(126,338)(127,331)(128,303)(129,321)
(130,309)(131,327)(132,315)(133,317)(134,305)(135,318)(136,311)(137,324)
(138,326)(139,314)(140,307)(141,320)(142,308)(143,310)(144,323)(145,316)
(146,304)(147,322)(148,319)(149,312)(150,325)(151,313)(152,306)(153,353)
(154,371)(155,359)(156,377)(157,365)(158,367)(159,355)(160,368)(161,361)
(162,374)(163,376)(164,364)(165,357)(166,370)(167,358)(168,360)(169,373)
(170,366)(171,354)(172,372)(173,369)(174,362)(175,375)(176,363)(177,356)
(178,378)(179,396)(180,384)(181,402)(182,390)(183,392)(184,380)(185,393)
(186,386)(187,399)(188,401)(189,389)(190,382)(191,395)(192,383)(193,385)
(194,398)(195,391)(196,379)(197,397)(198,394)(199,387)(200,400)(201,388)
(202,381);
poly := sub<Sym(402)|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, s3*s1*s2*s3*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

to this polytope