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Polytope of Type {400,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {400,2}*1600
if this polytope has a name.
Group : SmallGroup(1600,530)
Rank : 3
Schlafli Type : {400,2}
Number of vertices, edges, etc : 400, 400, 2
Order of s0s1s2 : 400
Order of s0s1s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {200,2}*800
   4-fold quotients : {100,2}*400
   5-fold quotients : {80,2}*320
   8-fold quotients : {50,2}*200
   10-fold quotients : {40,2}*160
   16-fold quotients : {25,2}*100
   20-fold quotients : {20,2}*80
   25-fold quotients : {16,2}*64
   40-fold quotients : {10,2}*40
   50-fold quotients : {8,2}*32
   80-fold quotients : {5,2}*20
   100-fold quotients : {4,2}*16
   200-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  2,  5)(  3,  4)(  6, 25)(  7, 24)(  8, 23)(  9, 22)( 10, 21)( 11, 20)
( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 27, 30)( 28, 29)( 31, 50)( 32, 49)
( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 42)( 40, 41)
( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 56,100)( 57, 99)( 58, 98)
( 59, 97)( 60, 96)( 61, 95)( 62, 94)( 63, 93)( 64, 92)( 65, 91)( 66, 90)
( 67, 89)( 68, 88)( 69, 87)( 70, 86)( 71, 85)( 72, 84)( 73, 83)( 74, 82)
( 75, 81)(101,151)(102,155)(103,154)(104,153)(105,152)(106,175)(107,174)
(108,173)(109,172)(110,171)(111,170)(112,169)(113,168)(114,167)(115,166)
(116,165)(117,164)(118,163)(119,162)(120,161)(121,160)(122,159)(123,158)
(124,157)(125,156)(126,176)(127,180)(128,179)(129,178)(130,177)(131,200)
(132,199)(133,198)(134,197)(135,196)(136,195)(137,194)(138,193)(139,192)
(140,191)(141,190)(142,189)(143,188)(144,187)(145,186)(146,185)(147,184)
(148,183)(149,182)(150,181)(201,301)(202,305)(203,304)(204,303)(205,302)
(206,325)(207,324)(208,323)(209,322)(210,321)(211,320)(212,319)(213,318)
(214,317)(215,316)(216,315)(217,314)(218,313)(219,312)(220,311)(221,310)
(222,309)(223,308)(224,307)(225,306)(226,326)(227,330)(228,329)(229,328)
(230,327)(231,350)(232,349)(233,348)(234,347)(235,346)(236,345)(237,344)
(238,343)(239,342)(240,341)(241,340)(242,339)(243,338)(244,337)(245,336)
(246,335)(247,334)(248,333)(249,332)(250,331)(251,376)(252,380)(253,379)
(254,378)(255,377)(256,400)(257,399)(258,398)(259,397)(260,396)(261,395)
(262,394)(263,393)(264,392)(265,391)(266,390)(267,389)(268,388)(269,387)
(270,386)(271,385)(272,384)(273,383)(274,382)(275,381)(276,351)(277,355)
(278,354)(279,353)(280,352)(281,375)(282,374)(283,373)(284,372)(285,371)
(286,370)(287,369)(288,368)(289,367)(290,366)(291,365)(292,364)(293,363)
(294,362)(295,361)(296,360)(297,359)(298,358)(299,357)(300,356);;
s1 := (  1,206)(  2,210)(  3,209)(  4,208)(  5,207)(  6,201)(  7,205)(  8,204)
(  9,203)( 10,202)( 11,225)( 12,224)( 13,223)( 14,222)( 15,221)( 16,220)
( 17,219)( 18,218)( 19,217)( 20,216)( 21,215)( 22,214)( 23,213)( 24,212)
( 25,211)( 26,231)( 27,235)( 28,234)( 29,233)( 30,232)( 31,226)( 32,230)
( 33,229)( 34,228)( 35,227)( 36,250)( 37,249)( 38,248)( 39,247)( 40,246)
( 41,245)( 42,244)( 43,243)( 44,242)( 45,241)( 46,240)( 47,239)( 48,238)
( 49,237)( 50,236)( 51,281)( 52,285)( 53,284)( 54,283)( 55,282)( 56,276)
( 57,280)( 58,279)( 59,278)( 60,277)( 61,300)( 62,299)( 63,298)( 64,297)
( 65,296)( 66,295)( 67,294)( 68,293)( 69,292)( 70,291)( 71,290)( 72,289)
( 73,288)( 74,287)( 75,286)( 76,256)( 77,260)( 78,259)( 79,258)( 80,257)
( 81,251)( 82,255)( 83,254)( 84,253)( 85,252)( 86,275)( 87,274)( 88,273)
( 89,272)( 90,271)( 91,270)( 92,269)( 93,268)( 94,267)( 95,266)( 96,265)
( 97,264)( 98,263)( 99,262)(100,261)(101,356)(102,360)(103,359)(104,358)
(105,357)(106,351)(107,355)(108,354)(109,353)(110,352)(111,375)(112,374)
(113,373)(114,372)(115,371)(116,370)(117,369)(118,368)(119,367)(120,366)
(121,365)(122,364)(123,363)(124,362)(125,361)(126,381)(127,385)(128,384)
(129,383)(130,382)(131,376)(132,380)(133,379)(134,378)(135,377)(136,400)
(137,399)(138,398)(139,397)(140,396)(141,395)(142,394)(143,393)(144,392)
(145,391)(146,390)(147,389)(148,388)(149,387)(150,386)(151,306)(152,310)
(153,309)(154,308)(155,307)(156,301)(157,305)(158,304)(159,303)(160,302)
(161,325)(162,324)(163,323)(164,322)(165,321)(166,320)(167,319)(168,318)
(169,317)(170,316)(171,315)(172,314)(173,313)(174,312)(175,311)(176,331)
(177,335)(178,334)(179,333)(180,332)(181,326)(182,330)(183,329)(184,328)
(185,327)(186,350)(187,349)(188,348)(189,347)(190,346)(191,345)(192,344)
(193,343)(194,342)(195,341)(196,340)(197,339)(198,338)(199,337)(200,336);;
s2 := (401,402);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(402)!(  2,  5)(  3,  4)(  6, 25)(  7, 24)(  8, 23)(  9, 22)( 10, 21)
( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 27, 30)( 28, 29)( 31, 50)
( 32, 49)( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 42)
( 40, 41)( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 56,100)( 57, 99)
( 58, 98)( 59, 97)( 60, 96)( 61, 95)( 62, 94)( 63, 93)( 64, 92)( 65, 91)
( 66, 90)( 67, 89)( 68, 88)( 69, 87)( 70, 86)( 71, 85)( 72, 84)( 73, 83)
( 74, 82)( 75, 81)(101,151)(102,155)(103,154)(104,153)(105,152)(106,175)
(107,174)(108,173)(109,172)(110,171)(111,170)(112,169)(113,168)(114,167)
(115,166)(116,165)(117,164)(118,163)(119,162)(120,161)(121,160)(122,159)
(123,158)(124,157)(125,156)(126,176)(127,180)(128,179)(129,178)(130,177)
(131,200)(132,199)(133,198)(134,197)(135,196)(136,195)(137,194)(138,193)
(139,192)(140,191)(141,190)(142,189)(143,188)(144,187)(145,186)(146,185)
(147,184)(148,183)(149,182)(150,181)(201,301)(202,305)(203,304)(204,303)
(205,302)(206,325)(207,324)(208,323)(209,322)(210,321)(211,320)(212,319)
(213,318)(214,317)(215,316)(216,315)(217,314)(218,313)(219,312)(220,311)
(221,310)(222,309)(223,308)(224,307)(225,306)(226,326)(227,330)(228,329)
(229,328)(230,327)(231,350)(232,349)(233,348)(234,347)(235,346)(236,345)
(237,344)(238,343)(239,342)(240,341)(241,340)(242,339)(243,338)(244,337)
(245,336)(246,335)(247,334)(248,333)(249,332)(250,331)(251,376)(252,380)
(253,379)(254,378)(255,377)(256,400)(257,399)(258,398)(259,397)(260,396)
(261,395)(262,394)(263,393)(264,392)(265,391)(266,390)(267,389)(268,388)
(269,387)(270,386)(271,385)(272,384)(273,383)(274,382)(275,381)(276,351)
(277,355)(278,354)(279,353)(280,352)(281,375)(282,374)(283,373)(284,372)
(285,371)(286,370)(287,369)(288,368)(289,367)(290,366)(291,365)(292,364)
(293,363)(294,362)(295,361)(296,360)(297,359)(298,358)(299,357)(300,356);
s1 := Sym(402)!(  1,206)(  2,210)(  3,209)(  4,208)(  5,207)(  6,201)(  7,205)
(  8,204)(  9,203)( 10,202)( 11,225)( 12,224)( 13,223)( 14,222)( 15,221)
( 16,220)( 17,219)( 18,218)( 19,217)( 20,216)( 21,215)( 22,214)( 23,213)
( 24,212)( 25,211)( 26,231)( 27,235)( 28,234)( 29,233)( 30,232)( 31,226)
( 32,230)( 33,229)( 34,228)( 35,227)( 36,250)( 37,249)( 38,248)( 39,247)
( 40,246)( 41,245)( 42,244)( 43,243)( 44,242)( 45,241)( 46,240)( 47,239)
( 48,238)( 49,237)( 50,236)( 51,281)( 52,285)( 53,284)( 54,283)( 55,282)
( 56,276)( 57,280)( 58,279)( 59,278)( 60,277)( 61,300)( 62,299)( 63,298)
( 64,297)( 65,296)( 66,295)( 67,294)( 68,293)( 69,292)( 70,291)( 71,290)
( 72,289)( 73,288)( 74,287)( 75,286)( 76,256)( 77,260)( 78,259)( 79,258)
( 80,257)( 81,251)( 82,255)( 83,254)( 84,253)( 85,252)( 86,275)( 87,274)
( 88,273)( 89,272)( 90,271)( 91,270)( 92,269)( 93,268)( 94,267)( 95,266)
( 96,265)( 97,264)( 98,263)( 99,262)(100,261)(101,356)(102,360)(103,359)
(104,358)(105,357)(106,351)(107,355)(108,354)(109,353)(110,352)(111,375)
(112,374)(113,373)(114,372)(115,371)(116,370)(117,369)(118,368)(119,367)
(120,366)(121,365)(122,364)(123,363)(124,362)(125,361)(126,381)(127,385)
(128,384)(129,383)(130,382)(131,376)(132,380)(133,379)(134,378)(135,377)
(136,400)(137,399)(138,398)(139,397)(140,396)(141,395)(142,394)(143,393)
(144,392)(145,391)(146,390)(147,389)(148,388)(149,387)(150,386)(151,306)
(152,310)(153,309)(154,308)(155,307)(156,301)(157,305)(158,304)(159,303)
(160,302)(161,325)(162,324)(163,323)(164,322)(165,321)(166,320)(167,319)
(168,318)(169,317)(170,316)(171,315)(172,314)(173,313)(174,312)(175,311)
(176,331)(177,335)(178,334)(179,333)(180,332)(181,326)(182,330)(183,329)
(184,328)(185,327)(186,350)(187,349)(188,348)(189,347)(190,346)(191,345)
(192,344)(193,343)(194,342)(195,341)(196,340)(197,339)(198,338)(199,337)
(200,336);
s2 := Sym(402)!(401,402);
poly := sub<Sym(402)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

to this polytope