Polytope of Type {4,182}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,182}*1456
Also Known As : {4,182|2}. if this polytope has another name.
Group : SmallGroup(1456,160)
Rank : 3
Schlafli Type : {4,182}
Number of vertices, edges, etc : 4, 364, 182
Order of s0s1s2 : 364
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 : {2,182}*728
4-fold quotients : {2,91}*364
7-fold quotients : {4,26}*208
13-fold quotients : {4,14}*112
14-fold quotients : {2,26}*104
26-fold quotients : {2,14}*56
28-fold quotients : {2,13}*52
52-fold quotients : {2,7}*28
91-fold quotients : {4,2}*16
182-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (183,274)(184,275)(185,276)(186,277)(187,278)(188,279)(189,280)(190,281)
(191,282)(192,283)(193,284)(194,285)(195,286)(196,287)(197,288)(198,289)
(199,290)(200,291)(201,292)(202,293)(203,294)(204,295)(205,296)(206,297)
(207,298)(208,299)(209,300)(210,301)(211,302)(212,303)(213,304)(214,305)
(215,306)(216,307)(217,308)(218,309)(219,310)(220,311)(221,312)(222,313)
(223,314)(224,315)(225,316)(226,317)(227,318)(228,319)(229,320)(230,321)
(231,322)(232,323)(233,324)(234,325)(235,326)(236,327)(237,328)(238,329)
(239,330)(240,331)(241,332)(242,333)(243,334)(244,335)(245,336)(246,337)
(247,338)(248,339)(249,340)(250,341)(251,342)(252,343)(253,344)(254,345)
(255,346)(256,347)(257,348)(258,349)(259,350)(260,351)(261,352)(262,353)
(263,354)(264,355)(265,356)(266,357)(267,358)(268,359)(269,360)(270,361)
(271,362)(272,363)(273,364);;
s1 := ( 1,183)( 2,195)( 3,194)( 4,193)( 5,192)( 6,191)( 7,190)( 8,189)
( 9,188)( 10,187)( 11,186)( 12,185)( 13,184)( 14,261)( 15,273)( 16,272)
( 17,271)( 18,270)( 19,269)( 20,268)( 21,267)( 22,266)( 23,265)( 24,264)
( 25,263)( 26,262)( 27,248)( 28,260)( 29,259)( 30,258)( 31,257)( 32,256)
( 33,255)( 34,254)( 35,253)( 36,252)( 37,251)( 38,250)( 39,249)( 40,235)
( 41,247)( 42,246)( 43,245)( 44,244)( 45,243)( 46,242)( 47,241)( 48,240)
( 49,239)( 50,238)( 51,237)( 52,236)( 53,222)( 54,234)( 55,233)( 56,232)
( 57,231)( 58,230)( 59,229)( 60,228)( 61,227)( 62,226)( 63,225)( 64,224)
( 65,223)( 66,209)( 67,221)( 68,220)( 69,219)( 70,218)( 71,217)( 72,216)
( 73,215)( 74,214)( 75,213)( 76,212)( 77,211)( 78,210)( 79,196)( 80,208)
( 81,207)( 82,206)( 83,205)( 84,204)( 85,203)( 86,202)( 87,201)( 88,200)
( 89,199)( 90,198)( 91,197)( 92,274)( 93,286)( 94,285)( 95,284)( 96,283)
( 97,282)( 98,281)( 99,280)(100,279)(101,278)(102,277)(103,276)(104,275)
(105,352)(106,364)(107,363)(108,362)(109,361)(110,360)(111,359)(112,358)
(113,357)(114,356)(115,355)(116,354)(117,353)(118,339)(119,351)(120,350)
(121,349)(122,348)(123,347)(124,346)(125,345)(126,344)(127,343)(128,342)
(129,341)(130,340)(131,326)(132,338)(133,337)(134,336)(135,335)(136,334)
(137,333)(138,332)(139,331)(140,330)(141,329)(142,328)(143,327)(144,313)
(145,325)(146,324)(147,323)(148,322)(149,321)(150,320)(151,319)(152,318)
(153,317)(154,316)(155,315)(156,314)(157,300)(158,312)(159,311)(160,310)
(161,309)(162,308)(163,307)(164,306)(165,305)(166,304)(167,303)(168,302)
(169,301)(170,287)(171,299)(172,298)(173,297)(174,296)(175,295)(176,294)
(177,293)(178,292)(179,291)(180,290)(181,289)(182,288);;
s2 := ( 1, 15)( 2, 14)( 3, 26)( 4, 25)( 5, 24)( 6, 23)( 7, 22)( 8, 21)
( 9, 20)( 10, 19)( 11, 18)( 12, 17)( 13, 16)( 27, 80)( 28, 79)( 29, 91)
( 30, 90)( 31, 89)( 32, 88)( 33, 87)( 34, 86)( 35, 85)( 36, 84)( 37, 83)
( 38, 82)( 39, 81)( 40, 67)( 41, 66)( 42, 78)( 43, 77)( 44, 76)( 45, 75)
( 46, 74)( 47, 73)( 48, 72)( 49, 71)( 50, 70)( 51, 69)( 52, 68)( 53, 54)
( 55, 65)( 56, 64)( 57, 63)( 58, 62)( 59, 61)( 92,106)( 93,105)( 94,117)
( 95,116)( 96,115)( 97,114)( 98,113)( 99,112)(100,111)(101,110)(102,109)
(103,108)(104,107)(118,171)(119,170)(120,182)(121,181)(122,180)(123,179)
(124,178)(125,177)(126,176)(127,175)(128,174)(129,173)(130,172)(131,158)
(132,157)(133,169)(134,168)(135,167)(136,166)(137,165)(138,164)(139,163)
(140,162)(141,161)(142,160)(143,159)(144,145)(146,156)(147,155)(148,154)
(149,153)(150,152)(183,197)(184,196)(185,208)(186,207)(187,206)(188,205)
(189,204)(190,203)(191,202)(192,201)(193,200)(194,199)(195,198)(209,262)
(210,261)(211,273)(212,272)(213,271)(214,270)(215,269)(216,268)(217,267)
(218,266)(219,265)(220,264)(221,263)(222,249)(223,248)(224,260)(225,259)
(226,258)(227,257)(228,256)(229,255)(230,254)(231,253)(232,252)(233,251)
(234,250)(235,236)(237,247)(238,246)(239,245)(240,244)(241,243)(274,288)
(275,287)(276,299)(277,298)(278,297)(279,296)(280,295)(281,294)(282,293)
(283,292)(284,291)(285,290)(286,289)(300,353)(301,352)(302,364)(303,363)
(304,362)(305,361)(306,360)(307,359)(308,358)(309,357)(310,356)(311,355)
(312,354)(313,340)(314,339)(315,351)(316,350)(317,349)(318,348)(319,347)
(320,346)(321,345)(322,344)(323,343)(324,342)(325,341)(326,327)(328,338)
(329,337)(330,336)(331,335)(332,334);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(364)!(183,274)(184,275)(185,276)(186,277)(187,278)(188,279)(189,280)
(190,281)(191,282)(192,283)(193,284)(194,285)(195,286)(196,287)(197,288)
(198,289)(199,290)(200,291)(201,292)(202,293)(203,294)(204,295)(205,296)
(206,297)(207,298)(208,299)(209,300)(210,301)(211,302)(212,303)(213,304)
(214,305)(215,306)(216,307)(217,308)(218,309)(219,310)(220,311)(221,312)
(222,313)(223,314)(224,315)(225,316)(226,317)(227,318)(228,319)(229,320)
(230,321)(231,322)(232,323)(233,324)(234,325)(235,326)(236,327)(237,328)
(238,329)(239,330)(240,331)(241,332)(242,333)(243,334)(244,335)(245,336)
(246,337)(247,338)(248,339)(249,340)(250,341)(251,342)(252,343)(253,344)
(254,345)(255,346)(256,347)(257,348)(258,349)(259,350)(260,351)(261,352)
(262,353)(263,354)(264,355)(265,356)(266,357)(267,358)(268,359)(269,360)
(270,361)(271,362)(272,363)(273,364);
s1 := Sym(364)!( 1,183)( 2,195)( 3,194)( 4,193)( 5,192)( 6,191)( 7,190)
( 8,189)( 9,188)( 10,187)( 11,186)( 12,185)( 13,184)( 14,261)( 15,273)
( 16,272)( 17,271)( 18,270)( 19,269)( 20,268)( 21,267)( 22,266)( 23,265)
( 24,264)( 25,263)( 26,262)( 27,248)( 28,260)( 29,259)( 30,258)( 31,257)
( 32,256)( 33,255)( 34,254)( 35,253)( 36,252)( 37,251)( 38,250)( 39,249)
( 40,235)( 41,247)( 42,246)( 43,245)( 44,244)( 45,243)( 46,242)( 47,241)
( 48,240)( 49,239)( 50,238)( 51,237)( 52,236)( 53,222)( 54,234)( 55,233)
( 56,232)( 57,231)( 58,230)( 59,229)( 60,228)( 61,227)( 62,226)( 63,225)
( 64,224)( 65,223)( 66,209)( 67,221)( 68,220)( 69,219)( 70,218)( 71,217)
( 72,216)( 73,215)( 74,214)( 75,213)( 76,212)( 77,211)( 78,210)( 79,196)
( 80,208)( 81,207)( 82,206)( 83,205)( 84,204)( 85,203)( 86,202)( 87,201)
( 88,200)( 89,199)( 90,198)( 91,197)( 92,274)( 93,286)( 94,285)( 95,284)
( 96,283)( 97,282)( 98,281)( 99,280)(100,279)(101,278)(102,277)(103,276)
(104,275)(105,352)(106,364)(107,363)(108,362)(109,361)(110,360)(111,359)
(112,358)(113,357)(114,356)(115,355)(116,354)(117,353)(118,339)(119,351)
(120,350)(121,349)(122,348)(123,347)(124,346)(125,345)(126,344)(127,343)
(128,342)(129,341)(130,340)(131,326)(132,338)(133,337)(134,336)(135,335)
(136,334)(137,333)(138,332)(139,331)(140,330)(141,329)(142,328)(143,327)
(144,313)(145,325)(146,324)(147,323)(148,322)(149,321)(150,320)(151,319)
(152,318)(153,317)(154,316)(155,315)(156,314)(157,300)(158,312)(159,311)
(160,310)(161,309)(162,308)(163,307)(164,306)(165,305)(166,304)(167,303)
(168,302)(169,301)(170,287)(171,299)(172,298)(173,297)(174,296)(175,295)
(176,294)(177,293)(178,292)(179,291)(180,290)(181,289)(182,288);
s2 := Sym(364)!( 1, 15)( 2, 14)( 3, 26)( 4, 25)( 5, 24)( 6, 23)( 7, 22)
( 8, 21)( 9, 20)( 10, 19)( 11, 18)( 12, 17)( 13, 16)( 27, 80)( 28, 79)
( 29, 91)( 30, 90)( 31, 89)( 32, 88)( 33, 87)( 34, 86)( 35, 85)( 36, 84)
( 37, 83)( 38, 82)( 39, 81)( 40, 67)( 41, 66)( 42, 78)( 43, 77)( 44, 76)
( 45, 75)( 46, 74)( 47, 73)( 48, 72)( 49, 71)( 50, 70)( 51, 69)( 52, 68)
( 53, 54)( 55, 65)( 56, 64)( 57, 63)( 58, 62)( 59, 61)( 92,106)( 93,105)
( 94,117)( 95,116)( 96,115)( 97,114)( 98,113)( 99,112)(100,111)(101,110)
(102,109)(103,108)(104,107)(118,171)(119,170)(120,182)(121,181)(122,180)
(123,179)(124,178)(125,177)(126,176)(127,175)(128,174)(129,173)(130,172)
(131,158)(132,157)(133,169)(134,168)(135,167)(136,166)(137,165)(138,164)
(139,163)(140,162)(141,161)(142,160)(143,159)(144,145)(146,156)(147,155)
(148,154)(149,153)(150,152)(183,197)(184,196)(185,208)(186,207)(187,206)
(188,205)(189,204)(190,203)(191,202)(192,201)(193,200)(194,199)(195,198)
(209,262)(210,261)(211,273)(212,272)(213,271)(214,270)(215,269)(216,268)
(217,267)(218,266)(219,265)(220,264)(221,263)(222,249)(223,248)(224,260)
(225,259)(226,258)(227,257)(228,256)(229,255)(230,254)(231,253)(232,252)
(233,251)(234,250)(235,236)(237,247)(238,246)(239,245)(240,244)(241,243)
(274,288)(275,287)(276,299)(277,298)(278,297)(279,296)(280,295)(281,294)
(282,293)(283,292)(284,291)(285,290)(286,289)(300,353)(301,352)(302,364)
(303,363)(304,362)(305,361)(306,360)(307,359)(308,358)(309,357)(310,356)
(311,355)(312,354)(313,340)(314,339)(315,351)(316,350)(317,349)(318,348)
(319,347)(320,346)(321,345)(322,344)(323,343)(324,342)(325,341)(326,327)
(328,338)(329,337)(330,336)(331,335)(332,334);
poly := sub<Sym(364)|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 >;
References : None.
to this polytope