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