Polytope of Type {380}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {380}*760
Also Known As : 380-gon, {380}. if this polytope has another name.
Group : SmallGroup(760,26)
Rank : 2
Schlafli Type : {380}
Number of vertices, edges, etc : 380, 380
Order of s₀s₁ : 380
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {380,2} of size 1520
Vertex Figure Of :
   {2,380} of size 1520
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {190}*380
   4-fold quotients : {95}*190
   5-fold quotients : {76}*152
   10-fold quotients : {38}*76
   19-fold quotients : {20}*40
   20-fold quotients : {19}*38
   38-fold quotients : {10}*20
   76-fold quotients : {5}*10
   95-fold quotients : {4}*8
   190-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {760}*1520
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope