Polytope of Type {2,390}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,390}*1560
if this polytope has a name.
Group : SmallGroup(1560,220)
Rank : 3
Schlafli Type : {2,390}
Number of vertices, edges, etc : 2, 390, 390
Order of s₀s₁s₂ : 390
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 : {2,195}*780
   3-fold quotients : {2,130}*520
   5-fold quotients : {2,78}*312
   6-fold quotients : {2,65}*260
   10-fold quotients : {2,39}*156
   13-fold quotients : {2,30}*120
   15-fold quotients : {2,26}*104
   26-fold quotients : {2,15}*60
   30-fold quotients : {2,13}*52
   39-fold quotients : {2,10}*40
   65-fold quotients : {2,6}*24
   78-fold quotients : {2,5}*20
   130-fold quotients : {2,3}*12
   195-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope