Polytope of Type {12,52}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,52}*1248
Also Known As : {12,52|2}. if this polytope has another name.
Group : SmallGroup(1248,729)
Rank : 3
Schlafli Type : {12,52}
Number of vertices, edges, etc : 12, 312, 52
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 : {12,26}*624, {6,52}*624a
3-fold quotients : {4,52}*416
4-fold quotients : {6,26}*312
6-fold quotients : {2,52}*208, {4,26}*208
12-fold quotients : {2,26}*104
13-fold quotients : {12,4}*96a
24-fold quotients : {2,13}*52
26-fold quotients : {12,2}*48, {6,4}*48a
39-fold quotients : {4,4}*32
52-fold quotients : {6,2}*24
78-fold quotients : {2,4}*16, {4,2}*16
104-fold quotients : {3,2}*12
156-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 14, 27)( 15, 28)( 16, 29)( 17, 30)( 18, 31)( 19, 32)( 20, 33)( 21, 34)
( 22, 35)( 23, 36)( 24, 37)( 25, 38)( 26, 39)( 53, 66)( 54, 67)( 55, 68)
( 56, 69)( 57, 70)( 58, 71)( 59, 72)( 60, 73)( 61, 74)( 62, 75)( 63, 76)
( 64, 77)( 65, 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)(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)(157,235)(158,236)(159,237)(160,238)
(161,239)(162,240)(163,241)(164,242)(165,243)(166,244)(167,245)(168,246)
(169,247)(170,261)(171,262)(172,263)(173,264)(174,265)(175,266)(176,267)
(177,268)(178,269)(179,270)(180,271)(181,272)(182,273)(183,248)(184,249)
(185,250)(186,251)(187,252)(188,253)(189,254)(190,255)(191,256)(192,257)
(193,258)(194,259)(195,260)(196,274)(197,275)(198,276)(199,277)(200,278)
(201,279)(202,280)(203,281)(204,282)(205,283)(206,284)(207,285)(208,286)
(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)(222,287)(223,288)(224,289)
(225,290)(226,291)(227,292)(228,293)(229,294)(230,295)(231,296)(232,297)
(233,298)(234,299);;
s1 := ( 1,170)( 2,182)( 3,181)( 4,180)( 5,179)( 6,178)( 7,177)( 8,176)
( 9,175)( 10,174)( 11,173)( 12,172)( 13,171)( 14,157)( 15,169)( 16,168)
( 17,167)( 18,166)( 19,165)( 20,164)( 21,163)( 22,162)( 23,161)( 24,160)
( 25,159)( 26,158)( 27,183)( 28,195)( 29,194)( 30,193)( 31,192)( 32,191)
( 33,190)( 34,189)( 35,188)( 36,187)( 37,186)( 38,185)( 39,184)( 40,209)
( 41,221)( 42,220)( 43,219)( 44,218)( 45,217)( 46,216)( 47,215)( 48,214)
( 49,213)( 50,212)( 51,211)( 52,210)( 53,196)( 54,208)( 55,207)( 56,206)
( 57,205)( 58,204)( 59,203)( 60,202)( 61,201)( 62,200)( 63,199)( 64,198)
( 65,197)( 66,222)( 67,234)( 68,233)( 69,232)( 70,231)( 71,230)( 72,229)
( 73,228)( 74,227)( 75,226)( 76,225)( 77,224)( 78,223)( 79,248)( 80,260)
( 81,259)( 82,258)( 83,257)( 84,256)( 85,255)( 86,254)( 87,253)( 88,252)
( 89,251)( 90,250)( 91,249)( 92,235)( 93,247)( 94,246)( 95,245)( 96,244)
( 97,243)( 98,242)( 99,241)(100,240)(101,239)(102,238)(103,237)(104,236)
(105,261)(106,273)(107,272)(108,271)(109,270)(110,269)(111,268)(112,267)
(113,266)(114,265)(115,264)(116,263)(117,262)(118,287)(119,299)(120,298)
(121,297)(122,296)(123,295)(124,294)(125,293)(126,292)(127,291)(128,290)
(129,289)(130,288)(131,274)(132,286)(133,285)(134,284)(135,283)(136,282)
(137,281)(138,280)(139,279)(140,278)(141,277)(142,276)(143,275)(144,300)
(145,312)(146,311)(147,310)(148,309)(149,308)(150,307)(151,306)(152,305)
(153,304)(154,303)(155,302)(156,301);;
s2 := ( 1, 2)( 3, 13)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 14, 15)( 16, 26)
( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 28)( 29, 39)( 30, 38)( 31, 37)
( 32, 36)( 33, 35)( 40, 41)( 42, 52)( 43, 51)( 44, 50)( 45, 49)( 46, 48)
( 53, 54)( 55, 65)( 56, 64)( 57, 63)( 58, 62)( 59, 61)( 66, 67)( 68, 78)
( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 79, 80)( 81, 91)( 82, 90)( 83, 89)
( 84, 88)( 85, 87)( 92, 93)( 94,104)( 95,103)( 96,102)( 97,101)( 98,100)
(105,106)(107,117)(108,116)(109,115)(110,114)(111,113)(118,119)(120,130)
(121,129)(122,128)(123,127)(124,126)(131,132)(133,143)(134,142)(135,141)
(136,140)(137,139)(144,145)(146,156)(147,155)(148,154)(149,153)(150,152)
(157,197)(158,196)(159,208)(160,207)(161,206)(162,205)(163,204)(164,203)
(165,202)(166,201)(167,200)(168,199)(169,198)(170,210)(171,209)(172,221)
(173,220)(174,219)(175,218)(176,217)(177,216)(178,215)(179,214)(180,213)
(181,212)(182,211)(183,223)(184,222)(185,234)(186,233)(187,232)(188,231)
(189,230)(190,229)(191,228)(192,227)(193,226)(194,225)(195,224)(235,275)
(236,274)(237,286)(238,285)(239,284)(240,283)(241,282)(242,281)(243,280)
(244,279)(245,278)(246,277)(247,276)(248,288)(249,287)(250,299)(251,298)
(252,297)(253,296)(254,295)(255,294)(256,293)(257,292)(258,291)(259,290)
(260,289)(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);;
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(312)!( 14, 27)( 15, 28)( 16, 29)( 17, 30)( 18, 31)( 19, 32)( 20, 33)
( 21, 34)( 22, 35)( 23, 36)( 24, 37)( 25, 38)( 26, 39)( 53, 66)( 54, 67)
( 55, 68)( 56, 69)( 57, 70)( 58, 71)( 59, 72)( 60, 73)( 61, 74)( 62, 75)
( 63, 76)( 64, 77)( 65, 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)
(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)(157,235)(158,236)(159,237)
(160,238)(161,239)(162,240)(163,241)(164,242)(165,243)(166,244)(167,245)
(168,246)(169,247)(170,261)(171,262)(172,263)(173,264)(174,265)(175,266)
(176,267)(177,268)(178,269)(179,270)(180,271)(181,272)(182,273)(183,248)
(184,249)(185,250)(186,251)(187,252)(188,253)(189,254)(190,255)(191,256)
(192,257)(193,258)(194,259)(195,260)(196,274)(197,275)(198,276)(199,277)
(200,278)(201,279)(202,280)(203,281)(204,282)(205,283)(206,284)(207,285)
(208,286)(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)(222,287)(223,288)
(224,289)(225,290)(226,291)(227,292)(228,293)(229,294)(230,295)(231,296)
(232,297)(233,298)(234,299);
s1 := Sym(312)!( 1,170)( 2,182)( 3,181)( 4,180)( 5,179)( 6,178)( 7,177)
( 8,176)( 9,175)( 10,174)( 11,173)( 12,172)( 13,171)( 14,157)( 15,169)
( 16,168)( 17,167)( 18,166)( 19,165)( 20,164)( 21,163)( 22,162)( 23,161)
( 24,160)( 25,159)( 26,158)( 27,183)( 28,195)( 29,194)( 30,193)( 31,192)
( 32,191)( 33,190)( 34,189)( 35,188)( 36,187)( 37,186)( 38,185)( 39,184)
( 40,209)( 41,221)( 42,220)( 43,219)( 44,218)( 45,217)( 46,216)( 47,215)
( 48,214)( 49,213)( 50,212)( 51,211)( 52,210)( 53,196)( 54,208)( 55,207)
( 56,206)( 57,205)( 58,204)( 59,203)( 60,202)( 61,201)( 62,200)( 63,199)
( 64,198)( 65,197)( 66,222)( 67,234)( 68,233)( 69,232)( 70,231)( 71,230)
( 72,229)( 73,228)( 74,227)( 75,226)( 76,225)( 77,224)( 78,223)( 79,248)
( 80,260)( 81,259)( 82,258)( 83,257)( 84,256)( 85,255)( 86,254)( 87,253)
( 88,252)( 89,251)( 90,250)( 91,249)( 92,235)( 93,247)( 94,246)( 95,245)
( 96,244)( 97,243)( 98,242)( 99,241)(100,240)(101,239)(102,238)(103,237)
(104,236)(105,261)(106,273)(107,272)(108,271)(109,270)(110,269)(111,268)
(112,267)(113,266)(114,265)(115,264)(116,263)(117,262)(118,287)(119,299)
(120,298)(121,297)(122,296)(123,295)(124,294)(125,293)(126,292)(127,291)
(128,290)(129,289)(130,288)(131,274)(132,286)(133,285)(134,284)(135,283)
(136,282)(137,281)(138,280)(139,279)(140,278)(141,277)(142,276)(143,275)
(144,300)(145,312)(146,311)(147,310)(148,309)(149,308)(150,307)(151,306)
(152,305)(153,304)(154,303)(155,302)(156,301);
s2 := Sym(312)!( 1, 2)( 3, 13)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 14, 15)
( 16, 26)( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 28)( 29, 39)( 30, 38)
( 31, 37)( 32, 36)( 33, 35)( 40, 41)( 42, 52)( 43, 51)( 44, 50)( 45, 49)
( 46, 48)( 53, 54)( 55, 65)( 56, 64)( 57, 63)( 58, 62)( 59, 61)( 66, 67)
( 68, 78)( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 79, 80)( 81, 91)( 82, 90)
( 83, 89)( 84, 88)( 85, 87)( 92, 93)( 94,104)( 95,103)( 96,102)( 97,101)
( 98,100)(105,106)(107,117)(108,116)(109,115)(110,114)(111,113)(118,119)
(120,130)(121,129)(122,128)(123,127)(124,126)(131,132)(133,143)(134,142)
(135,141)(136,140)(137,139)(144,145)(146,156)(147,155)(148,154)(149,153)
(150,152)(157,197)(158,196)(159,208)(160,207)(161,206)(162,205)(163,204)
(164,203)(165,202)(166,201)(167,200)(168,199)(169,198)(170,210)(171,209)
(172,221)(173,220)(174,219)(175,218)(176,217)(177,216)(178,215)(179,214)
(180,213)(181,212)(182,211)(183,223)(184,222)(185,234)(186,233)(187,232)
(188,231)(189,230)(190,229)(191,228)(192,227)(193,226)(194,225)(195,224)
(235,275)(236,274)(237,286)(238,285)(239,284)(240,283)(241,282)(242,281)
(243,280)(244,279)(245,278)(246,277)(247,276)(248,288)(249,287)(250,299)
(251,298)(252,297)(253,296)(254,295)(255,294)(256,293)(257,292)(258,291)
(259,290)(260,289)(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);
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,
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