Polytope of Type {4,190}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,190}*1520
Also Known As : {4,190|2}. if this polytope has another name.
Group : SmallGroup(1520,160)
Rank : 3
Schlafli Type : {4,190}
Number of vertices, edges, etc : 4, 380, 190
Order of s0s1s2 : 380
Order of s0s1s2s1 : 2
Special Properties :
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 : {4,38}*304
10-fold quotients : {2,38}*152
19-fold quotients : {4,10}*80
20-fold quotients : {2,19}*76
38-fold quotients : {2,10}*40
76-fold quotients : {2,5}*20
95-fold quotients : {4,2}*16
190-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (191,286)(192,287)(193,288)(194,289)(195,290)(196,291)(197,292)(198,293)
(199,294)(200,295)(201,296)(202,297)(203,298)(204,299)(205,300)(206,301)
(207,302)(208,303)(209,304)(210,305)(211,306)(212,307)(213,308)(214,309)
(215,310)(216,311)(217,312)(218,313)(219,314)(220,315)(221,316)(222,317)
(223,318)(224,319)(225,320)(226,321)(227,322)(228,323)(229,324)(230,325)
(231,326)(232,327)(233,328)(234,329)(235,330)(236,331)(237,332)(238,333)
(239,334)(240,335)(241,336)(242,337)(243,338)(244,339)(245,340)(246,341)
(247,342)(248,343)(249,344)(250,345)(251,346)(252,347)(253,348)(254,349)
(255,350)(256,351)(257,352)(258,353)(259,354)(260,355)(261,356)(262,357)
(263,358)(264,359)(265,360)(266,361)(267,362)(268,363)(269,364)(270,365)
(271,366)(272,367)(273,368)(274,369)(275,370)(276,371)(277,372)(278,373)
(279,374)(280,375)(281,376)(282,377)(283,378)(284,379)(285,380);;
s1 := ( 1,191)( 2,209)( 3,208)( 4,207)( 5,206)( 6,205)( 7,204)( 8,203)
( 9,202)( 10,201)( 11,200)( 12,199)( 13,198)( 14,197)( 15,196)( 16,195)
( 17,194)( 18,193)( 19,192)( 20,267)( 21,285)( 22,284)( 23,283)( 24,282)
( 25,281)( 26,280)( 27,279)( 28,278)( 29,277)( 30,276)( 31,275)( 32,274)
( 33,273)( 34,272)( 35,271)( 36,270)( 37,269)( 38,268)( 39,248)( 40,266)
( 41,265)( 42,264)( 43,263)( 44,262)( 45,261)( 46,260)( 47,259)( 48,258)
( 49,257)( 50,256)( 51,255)( 52,254)( 53,253)( 54,252)( 55,251)( 56,250)
( 57,249)( 58,229)( 59,247)( 60,246)( 61,245)( 62,244)( 63,243)( 64,242)
( 65,241)( 66,240)( 67,239)( 68,238)( 69,237)( 70,236)( 71,235)( 72,234)
( 73,233)( 74,232)( 75,231)( 76,230)( 77,210)( 78,228)( 79,227)( 80,226)
( 81,225)( 82,224)( 83,223)( 84,222)( 85,221)( 86,220)( 87,219)( 88,218)
( 89,217)( 90,216)( 91,215)( 92,214)( 93,213)( 94,212)( 95,211)( 96,286)
( 97,304)( 98,303)( 99,302)(100,301)(101,300)(102,299)(103,298)(104,297)
(105,296)(106,295)(107,294)(108,293)(109,292)(110,291)(111,290)(112,289)
(113,288)(114,287)(115,362)(116,380)(117,379)(118,378)(119,377)(120,376)
(121,375)(122,374)(123,373)(124,372)(125,371)(126,370)(127,369)(128,368)
(129,367)(130,366)(131,365)(132,364)(133,363)(134,343)(135,361)(136,360)
(137,359)(138,358)(139,357)(140,356)(141,355)(142,354)(143,353)(144,352)
(145,351)(146,350)(147,349)(148,348)(149,347)(150,346)(151,345)(152,344)
(153,324)(154,342)(155,341)(156,340)(157,339)(158,338)(159,337)(160,336)
(161,335)(162,334)(163,333)(164,332)(165,331)(166,330)(167,329)(168,328)
(169,327)(170,326)(171,325)(172,305)(173,323)(174,322)(175,321)(176,320)
(177,319)(178,318)(179,317)(180,316)(181,315)(182,314)(183,313)(184,312)
(185,311)(186,310)(187,309)(188,308)(189,307)(190,306);;
s2 := ( 1, 21)( 2, 20)( 3, 38)( 4, 37)( 5, 36)( 6, 35)( 7, 34)( 8, 33)
( 9, 32)( 10, 31)( 11, 30)( 12, 29)( 13, 28)( 14, 27)( 15, 26)( 16, 25)
( 17, 24)( 18, 23)( 19, 22)( 39, 78)( 40, 77)( 41, 95)( 42, 94)( 43, 93)
( 44, 92)( 45, 91)( 46, 90)( 47, 89)( 48, 88)( 49, 87)( 50, 86)( 51, 85)
( 52, 84)( 53, 83)( 54, 82)( 55, 81)( 56, 80)( 57, 79)( 58, 59)( 60, 76)
( 61, 75)( 62, 74)( 63, 73)( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 96,116)
( 97,115)( 98,133)( 99,132)(100,131)(101,130)(102,129)(103,128)(104,127)
(105,126)(106,125)(107,124)(108,123)(109,122)(110,121)(111,120)(112,119)
(113,118)(114,117)(134,173)(135,172)(136,190)(137,189)(138,188)(139,187)
(140,186)(141,185)(142,184)(143,183)(144,182)(145,181)(146,180)(147,179)
(148,178)(149,177)(150,176)(151,175)(152,174)(153,154)(155,171)(156,170)
(157,169)(158,168)(159,167)(160,166)(161,165)(162,164)(191,211)(192,210)
(193,228)(194,227)(195,226)(196,225)(197,224)(198,223)(199,222)(200,221)
(201,220)(202,219)(203,218)(204,217)(205,216)(206,215)(207,214)(208,213)
(209,212)(229,268)(230,267)(231,285)(232,284)(233,283)(234,282)(235,281)
(236,280)(237,279)(238,278)(239,277)(240,276)(241,275)(242,274)(243,273)
(244,272)(245,271)(246,270)(247,269)(248,249)(250,266)(251,265)(252,264)
(253,263)(254,262)(255,261)(256,260)(257,259)(286,306)(287,305)(288,323)
(289,322)(290,321)(291,320)(292,319)(293,318)(294,317)(295,316)(296,315)
(297,314)(298,313)(299,312)(300,311)(301,310)(302,309)(303,308)(304,307)
(324,363)(325,362)(326,380)(327,379)(328,378)(329,377)(330,376)(331,375)
(332,374)(333,373)(334,372)(335,371)(336,370)(337,369)(338,368)(339,367)
(340,366)(341,365)(342,364)(343,344)(345,361)(346,360)(347,359)(348,358)
(349,357)(350,356)(351,355)(352,354);;
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, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(380)!(191,286)(192,287)(193,288)(194,289)(195,290)(196,291)(197,292)
(198,293)(199,294)(200,295)(201,296)(202,297)(203,298)(204,299)(205,300)
(206,301)(207,302)(208,303)(209,304)(210,305)(211,306)(212,307)(213,308)
(214,309)(215,310)(216,311)(217,312)(218,313)(219,314)(220,315)(221,316)
(222,317)(223,318)(224,319)(225,320)(226,321)(227,322)(228,323)(229,324)
(230,325)(231,326)(232,327)(233,328)(234,329)(235,330)(236,331)(237,332)
(238,333)(239,334)(240,335)(241,336)(242,337)(243,338)(244,339)(245,340)
(246,341)(247,342)(248,343)(249,344)(250,345)(251,346)(252,347)(253,348)
(254,349)(255,350)(256,351)(257,352)(258,353)(259,354)(260,355)(261,356)
(262,357)(263,358)(264,359)(265,360)(266,361)(267,362)(268,363)(269,364)
(270,365)(271,366)(272,367)(273,368)(274,369)(275,370)(276,371)(277,372)
(278,373)(279,374)(280,375)(281,376)(282,377)(283,378)(284,379)(285,380);
s1 := Sym(380)!( 1,191)( 2,209)( 3,208)( 4,207)( 5,206)( 6,205)( 7,204)
( 8,203)( 9,202)( 10,201)( 11,200)( 12,199)( 13,198)( 14,197)( 15,196)
( 16,195)( 17,194)( 18,193)( 19,192)( 20,267)( 21,285)( 22,284)( 23,283)
( 24,282)( 25,281)( 26,280)( 27,279)( 28,278)( 29,277)( 30,276)( 31,275)
( 32,274)( 33,273)( 34,272)( 35,271)( 36,270)( 37,269)( 38,268)( 39,248)
( 40,266)( 41,265)( 42,264)( 43,263)( 44,262)( 45,261)( 46,260)( 47,259)
( 48,258)( 49,257)( 50,256)( 51,255)( 52,254)( 53,253)( 54,252)( 55,251)
( 56,250)( 57,249)( 58,229)( 59,247)( 60,246)( 61,245)( 62,244)( 63,243)
( 64,242)( 65,241)( 66,240)( 67,239)( 68,238)( 69,237)( 70,236)( 71,235)
( 72,234)( 73,233)( 74,232)( 75,231)( 76,230)( 77,210)( 78,228)( 79,227)
( 80,226)( 81,225)( 82,224)( 83,223)( 84,222)( 85,221)( 86,220)( 87,219)
( 88,218)( 89,217)( 90,216)( 91,215)( 92,214)( 93,213)( 94,212)( 95,211)
( 96,286)( 97,304)( 98,303)( 99,302)(100,301)(101,300)(102,299)(103,298)
(104,297)(105,296)(106,295)(107,294)(108,293)(109,292)(110,291)(111,290)
(112,289)(113,288)(114,287)(115,362)(116,380)(117,379)(118,378)(119,377)
(120,376)(121,375)(122,374)(123,373)(124,372)(125,371)(126,370)(127,369)
(128,368)(129,367)(130,366)(131,365)(132,364)(133,363)(134,343)(135,361)
(136,360)(137,359)(138,358)(139,357)(140,356)(141,355)(142,354)(143,353)
(144,352)(145,351)(146,350)(147,349)(148,348)(149,347)(150,346)(151,345)
(152,344)(153,324)(154,342)(155,341)(156,340)(157,339)(158,338)(159,337)
(160,336)(161,335)(162,334)(163,333)(164,332)(165,331)(166,330)(167,329)
(168,328)(169,327)(170,326)(171,325)(172,305)(173,323)(174,322)(175,321)
(176,320)(177,319)(178,318)(179,317)(180,316)(181,315)(182,314)(183,313)
(184,312)(185,311)(186,310)(187,309)(188,308)(189,307)(190,306);
s2 := Sym(380)!( 1, 21)( 2, 20)( 3, 38)( 4, 37)( 5, 36)( 6, 35)( 7, 34)
( 8, 33)( 9, 32)( 10, 31)( 11, 30)( 12, 29)( 13, 28)( 14, 27)( 15, 26)
( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 39, 78)( 40, 77)( 41, 95)( 42, 94)
( 43, 93)( 44, 92)( 45, 91)( 46, 90)( 47, 89)( 48, 88)( 49, 87)( 50, 86)
( 51, 85)( 52, 84)( 53, 83)( 54, 82)( 55, 81)( 56, 80)( 57, 79)( 58, 59)
( 60, 76)( 61, 75)( 62, 74)( 63, 73)( 64, 72)( 65, 71)( 66, 70)( 67, 69)
( 96,116)( 97,115)( 98,133)( 99,132)(100,131)(101,130)(102,129)(103,128)
(104,127)(105,126)(106,125)(107,124)(108,123)(109,122)(110,121)(111,120)
(112,119)(113,118)(114,117)(134,173)(135,172)(136,190)(137,189)(138,188)
(139,187)(140,186)(141,185)(142,184)(143,183)(144,182)(145,181)(146,180)
(147,179)(148,178)(149,177)(150,176)(151,175)(152,174)(153,154)(155,171)
(156,170)(157,169)(158,168)(159,167)(160,166)(161,165)(162,164)(191,211)
(192,210)(193,228)(194,227)(195,226)(196,225)(197,224)(198,223)(199,222)
(200,221)(201,220)(202,219)(203,218)(204,217)(205,216)(206,215)(207,214)
(208,213)(209,212)(229,268)(230,267)(231,285)(232,284)(233,283)(234,282)
(235,281)(236,280)(237,279)(238,278)(239,277)(240,276)(241,275)(242,274)
(243,273)(244,272)(245,271)(246,270)(247,269)(248,249)(250,266)(251,265)
(252,264)(253,263)(254,262)(255,261)(256,260)(257,259)(286,306)(287,305)
(288,323)(289,322)(290,321)(291,320)(292,319)(293,318)(294,317)(295,316)
(296,315)(297,314)(298,313)(299,312)(300,311)(301,310)(302,309)(303,308)
(304,307)(324,363)(325,362)(326,380)(327,379)(328,378)(329,377)(330,376)
(331,375)(332,374)(333,373)(334,372)(335,371)(336,370)(337,369)(338,368)
(339,367)(340,366)(341,365)(342,364)(343,344)(345,361)(346,360)(347,359)
(348,358)(349,357)(350,356)(351,355)(352,354);
poly := sub<Sym(380)|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, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope