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