Polytope of Type {2,380}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,380}*1520
if this polytope has a name.
Group : SmallGroup(1520,158)
Rank : 3
Schlafli Type : {2,380}
Number of vertices, edges, etc : 2, 380, 380
Order of s₀s₁s₂ : 380
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 : {2,190}*760
   4-fold quotients : {2,95}*380
   5-fold quotients : {2,76}*304
   10-fold quotients : {2,38}*152
   19-fold quotients : {2,20}*80
   20-fold quotients : {2,19}*76
   38-fold quotients : {2,10}*40
   76-fold quotients : {2,5}*20
   95-fold quotients : {2,4}*16
   190-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope