Polytope of Type {2,400}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,400}*1600
if this polytope has a name.
Group : SmallGroup(1600,530)
Rank : 3
Schlafli Type : {2,400}
Number of vertices, edges, etc : 2, 400, 400
Order of s₀s₁s₂ : 400
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {2,200}*800
   4-fold quotients : {2,100}*400
   5-fold quotients : {2,80}*320
   8-fold quotients : {2,50}*200
   10-fold quotients : {2,40}*160
   16-fold quotients : {2,25}*100
   20-fold quotients : {2,20}*80
   25-fold quotients : {2,16}*64
   40-fold quotients : {2,10}*40
   50-fold quotients : {2,8}*32
   80-fold quotients : {2,5}*20
   100-fold quotients : {2,4}*16
   200-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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