Polytope of Type {52,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {52,12}*1248
Also Known As : {52,12|2}. if this polytope has another name.
Group : SmallGroup(1248,729)
Rank : 3
Schlafli Type : {52,12}
Number of vertices, edges, etc : 52, 312, 12
Order of s0s1s2 : 156
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 : {26,12}*624, {52,6}*624a
3-fold quotients : {52,4}*416
4-fold quotients : {26,6}*312
6-fold quotients : {52,2}*208, {26,4}*208
12-fold quotients : {26,2}*104
13-fold quotients : {4,12}*96a
24-fold quotients : {13,2}*52
26-fold quotients : {2,12}*48, {4,6}*48a
39-fold quotients : {4,4}*32
52-fold quotients : {2,6}*24
78-fold quotients : {2,4}*16, {4,2}*16
104-fold quotients : {2,3}*12
156-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)
(157,196)(158,208)(159,207)(160,206)(161,205)(162,204)(163,203)(164,202)
(165,201)(166,200)(167,199)(168,198)(169,197)(170,209)(171,221)(172,220)
(173,219)(174,218)(175,217)(176,216)(177,215)(178,214)(179,213)(180,212)
(181,211)(182,210)(183,222)(184,234)(185,233)(186,232)(187,231)(188,230)
(189,229)(190,228)(191,227)(192,226)(193,225)(194,224)(195,223)(235,274)
(236,286)(237,285)(238,284)(239,283)(240,282)(241,281)(242,280)(243,279)
(244,278)(245,277)(246,276)(247,275)(248,287)(249,299)(250,298)(251,297)
(252,296)(253,295)(254,294)(255,293)(256,292)(257,291)(258,290)(259,289)
(260,288)(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);;
s1 := ( 1,158)( 2,157)( 3,169)( 4,168)( 5,167)( 6,166)( 7,165)( 8,164)
( 9,163)( 10,162)( 11,161)( 12,160)( 13,159)( 14,184)( 15,183)( 16,195)
( 17,194)( 18,193)( 19,192)( 20,191)( 21,190)( 22,189)( 23,188)( 24,187)
( 25,186)( 26,185)( 27,171)( 28,170)( 29,182)( 30,181)( 31,180)( 32,179)
( 33,178)( 34,177)( 35,176)( 36,175)( 37,174)( 38,173)( 39,172)( 40,197)
( 41,196)( 42,208)( 43,207)( 44,206)( 45,205)( 46,204)( 47,203)( 48,202)
( 49,201)( 50,200)( 51,199)( 52,198)( 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)( 79,236)( 80,235)
( 81,247)( 82,246)( 83,245)( 84,244)( 85,243)( 86,242)( 87,241)( 88,240)
( 89,239)( 90,238)( 91,237)( 92,262)( 93,261)( 94,273)( 95,272)( 96,271)
( 97,270)( 98,269)( 99,268)(100,267)(101,266)(102,265)(103,264)(104,263)
(105,249)(106,248)(107,260)(108,259)(109,258)(110,257)(111,256)(112,255)
(113,254)(114,253)(115,252)(116,251)(117,250)(118,275)(119,274)(120,286)
(121,285)(122,284)(123,283)(124,282)(125,281)(126,280)(127,279)(128,278)
(129,277)(130,276)(131,301)(132,300)(133,312)(134,311)(135,310)(136,309)
(137,308)(138,307)(139,306)(140,305)(141,304)(142,303)(143,302)(144,288)
(145,287)(146,299)(147,298)(148,297)(149,296)(150,295)(151,294)(152,293)
(153,292)(154,291)(155,290)(156,289);;
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)( 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)( 79, 92)( 80, 93)( 81, 94)( 82, 95)( 83, 96)( 84, 97)
( 85, 98)( 86, 99)( 87,100)( 88,101)( 89,102)( 90,103)( 91,104)(118,131)
(119,132)(120,133)(121,134)(122,135)(123,136)(124,137)(125,138)(126,139)
(127,140)(128,141)(129,142)(130,143)(157,248)(158,249)(159,250)(160,251)
(161,252)(162,253)(163,254)(164,255)(165,256)(166,257)(167,258)(168,259)
(169,260)(170,235)(171,236)(172,237)(173,238)(174,239)(175,240)(176,241)
(177,242)(178,243)(179,244)(180,245)(181,246)(182,247)(183,261)(184,262)
(185,263)(186,264)(187,265)(188,266)(189,267)(190,268)(191,269)(192,270)
(193,271)(194,272)(195,273)(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)
(209,274)(210,275)(211,276)(212,277)(213,278)(214,279)(215,280)(216,281)
(217,282)(218,283)(219,284)(220,285)(221,286)(222,300)(223,301)(224,302)
(225,303)(226,304)(227,305)(228,306)(229,307)(230,308)(231,309)(232,310)
(233,311)(234,312);;
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(312)!( 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)(157,196)(158,208)(159,207)(160,206)(161,205)(162,204)(163,203)
(164,202)(165,201)(166,200)(167,199)(168,198)(169,197)(170,209)(171,221)
(172,220)(173,219)(174,218)(175,217)(176,216)(177,215)(178,214)(179,213)
(180,212)(181,211)(182,210)(183,222)(184,234)(185,233)(186,232)(187,231)
(188,230)(189,229)(190,228)(191,227)(192,226)(193,225)(194,224)(195,223)
(235,274)(236,286)(237,285)(238,284)(239,283)(240,282)(241,281)(242,280)
(243,279)(244,278)(245,277)(246,276)(247,275)(248,287)(249,299)(250,298)
(251,297)(252,296)(253,295)(254,294)(255,293)(256,292)(257,291)(258,290)
(259,289)(260,288)(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);
s1 := Sym(312)!( 1,158)( 2,157)( 3,169)( 4,168)( 5,167)( 6,166)( 7,165)
( 8,164)( 9,163)( 10,162)( 11,161)( 12,160)( 13,159)( 14,184)( 15,183)
( 16,195)( 17,194)( 18,193)( 19,192)( 20,191)( 21,190)( 22,189)( 23,188)
( 24,187)( 25,186)( 26,185)( 27,171)( 28,170)( 29,182)( 30,181)( 31,180)
( 32,179)( 33,178)( 34,177)( 35,176)( 36,175)( 37,174)( 38,173)( 39,172)
( 40,197)( 41,196)( 42,208)( 43,207)( 44,206)( 45,205)( 46,204)( 47,203)
( 48,202)( 49,201)( 50,200)( 51,199)( 52,198)( 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)( 79,236)
( 80,235)( 81,247)( 82,246)( 83,245)( 84,244)( 85,243)( 86,242)( 87,241)
( 88,240)( 89,239)( 90,238)( 91,237)( 92,262)( 93,261)( 94,273)( 95,272)
( 96,271)( 97,270)( 98,269)( 99,268)(100,267)(101,266)(102,265)(103,264)
(104,263)(105,249)(106,248)(107,260)(108,259)(109,258)(110,257)(111,256)
(112,255)(113,254)(114,253)(115,252)(116,251)(117,250)(118,275)(119,274)
(120,286)(121,285)(122,284)(123,283)(124,282)(125,281)(126,280)(127,279)
(128,278)(129,277)(130,276)(131,301)(132,300)(133,312)(134,311)(135,310)
(136,309)(137,308)(138,307)(139,306)(140,305)(141,304)(142,303)(143,302)
(144,288)(145,287)(146,299)(147,298)(148,297)(149,296)(150,295)(151,294)
(152,293)(153,292)(154,291)(155,290)(156,289);
s2 := Sym(312)!( 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)( 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)( 79, 92)( 80, 93)( 81, 94)( 82, 95)( 83, 96)
( 84, 97)( 85, 98)( 86, 99)( 87,100)( 88,101)( 89,102)( 90,103)( 91,104)
(118,131)(119,132)(120,133)(121,134)(122,135)(123,136)(124,137)(125,138)
(126,139)(127,140)(128,141)(129,142)(130,143)(157,248)(158,249)(159,250)
(160,251)(161,252)(162,253)(163,254)(164,255)(165,256)(166,257)(167,258)
(168,259)(169,260)(170,235)(171,236)(172,237)(173,238)(174,239)(175,240)
(176,241)(177,242)(178,243)(179,244)(180,245)(181,246)(182,247)(183,261)
(184,262)(185,263)(186,264)(187,265)(188,266)(189,267)(190,268)(191,269)
(192,270)(193,271)(194,272)(195,273)(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)(209,274)(210,275)(211,276)(212,277)(213,278)(214,279)(215,280)
(216,281)(217,282)(218,283)(219,284)(220,285)(221,286)(222,300)(223,301)
(224,302)(225,303)(226,304)(227,305)(228,306)(229,307)(230,308)(231,309)
(232,310)(233,311)(234,312);
poly := sub<Sym(312)|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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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