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