Polytope of Type {2,8,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,10}*1600
if this polytope has a name.
Group : SmallGroup(1600,10010)
Rank : 4
Schlafli Type : {2,8,10}
Number of vertices, edges, etc : 2, 40, 200, 50
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 : {2,4,10}*800
   4-fold quotients : {2,4,10}*400
   25-fold quotients : {2,8,2}*64
   50-fold quotients : {2,4,2}*32
   100-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope