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Polytope of Type {12,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6,6}*1152a
if this polytope has a name.
Group : SmallGroup(1152,157550)
Rank : 4
Schlafli Type : {12,6,6}
Number of vertices, edges, etc : 12, 48, 24, 8
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   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 : {12,6,3}*576, {6,6,6}*576a
   3-fold quotients : {4,6,6}*384
   4-fold quotients : {6,6,3}*288
   6-fold quotients : {4,6,3}*192, {2,6,6}*192
   12-fold quotients : {12,2,2}*96, {2,3,6}*96, {2,6,3}*96
   24-fold quotients : {2,3,3}*48, {6,2,2}*48
   36-fold quotients : {4,2,2}*32
   48-fold quotients : {3,2,2}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  5,  9)(  6, 10)(  7, 11)(  8, 12)( 17, 21)( 18, 22)( 19, 23)( 20, 24)
( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 41, 45)( 42, 46)( 43, 47)( 44, 48)
( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 65, 69)( 66, 70)( 67, 71)( 68, 72)
( 73,109)( 74,110)( 75,111)( 76,112)( 77,117)( 78,118)( 79,119)( 80,120)
( 81,113)( 82,114)( 83,115)( 84,116)( 85,121)( 86,122)( 87,123)( 88,124)
( 89,129)( 90,130)( 91,131)( 92,132)( 93,125)( 94,126)( 95,127)( 96,128)
( 97,133)( 98,134)( 99,135)(100,136)(101,141)(102,142)(103,143)(104,144)
(105,137)(106,138)(107,139)(108,140)(149,153)(150,154)(151,155)(152,156)
(161,165)(162,166)(163,167)(164,168)(173,177)(174,178)(175,179)(176,180)
(185,189)(186,190)(187,191)(188,192)(197,201)(198,202)(199,203)(200,204)
(209,213)(210,214)(211,215)(212,216)(217,253)(218,254)(219,255)(220,256)
(221,261)(222,262)(223,263)(224,264)(225,257)(226,258)(227,259)(228,260)
(229,265)(230,266)(231,267)(232,268)(233,273)(234,274)(235,275)(236,276)
(237,269)(238,270)(239,271)(240,272)(241,277)(242,278)(243,279)(244,280)
(245,285)(246,286)(247,287)(248,288)(249,281)(250,282)(251,283)(252,284);;
s1 := (  1, 77)(  2, 78)(  3, 80)(  4, 79)(  5, 73)(  6, 74)(  7, 76)(  8, 75)
(  9, 81)( 10, 82)( 11, 84)( 12, 83)( 13,101)( 14,102)( 15,104)( 16,103)
( 17, 97)( 18, 98)( 19,100)( 20, 99)( 21,105)( 22,106)( 23,108)( 24,107)
( 25, 89)( 26, 90)( 27, 92)( 28, 91)( 29, 85)( 30, 86)( 31, 88)( 32, 87)
( 33, 93)( 34, 94)( 35, 96)( 36, 95)( 37,113)( 38,114)( 39,116)( 40,115)
( 41,109)( 42,110)( 43,112)( 44,111)( 45,117)( 46,118)( 47,120)( 48,119)
( 49,137)( 50,138)( 51,140)( 52,139)( 53,133)( 54,134)( 55,136)( 56,135)
( 57,141)( 58,142)( 59,144)( 60,143)( 61,125)( 62,126)( 63,128)( 64,127)
( 65,121)( 66,122)( 67,124)( 68,123)( 69,129)( 70,130)( 71,132)( 72,131)
(145,221)(146,222)(147,224)(148,223)(149,217)(150,218)(151,220)(152,219)
(153,225)(154,226)(155,228)(156,227)(157,245)(158,246)(159,248)(160,247)
(161,241)(162,242)(163,244)(164,243)(165,249)(166,250)(167,252)(168,251)
(169,233)(170,234)(171,236)(172,235)(173,229)(174,230)(175,232)(176,231)
(177,237)(178,238)(179,240)(180,239)(181,257)(182,258)(183,260)(184,259)
(185,253)(186,254)(187,256)(188,255)(189,261)(190,262)(191,264)(192,263)
(193,281)(194,282)(195,284)(196,283)(197,277)(198,278)(199,280)(200,279)
(201,285)(202,286)(203,288)(204,287)(205,269)(206,270)(207,272)(208,271)
(209,265)(210,266)(211,268)(212,267)(213,273)(214,274)(215,276)(216,275);;
s2 := (  1, 13)(  2, 16)(  3, 15)(  4, 14)(  5, 17)(  6, 20)(  7, 19)(  8, 18)
(  9, 21)( 10, 24)( 11, 23)( 12, 22)( 26, 28)( 30, 32)( 34, 36)( 37, 49)
( 38, 52)( 39, 51)( 40, 50)( 41, 53)( 42, 56)( 43, 55)( 44, 54)( 45, 57)
( 46, 60)( 47, 59)( 48, 58)( 62, 64)( 66, 68)( 70, 72)( 73, 85)( 74, 88)
( 75, 87)( 76, 86)( 77, 89)( 78, 92)( 79, 91)( 80, 90)( 81, 93)( 82, 96)
( 83, 95)( 84, 94)( 98,100)(102,104)(106,108)(109,121)(110,124)(111,123)
(112,122)(113,125)(114,128)(115,127)(116,126)(117,129)(118,132)(119,131)
(120,130)(134,136)(138,140)(142,144)(145,157)(146,160)(147,159)(148,158)
(149,161)(150,164)(151,163)(152,162)(153,165)(154,168)(155,167)(156,166)
(170,172)(174,176)(178,180)(181,193)(182,196)(183,195)(184,194)(185,197)
(186,200)(187,199)(188,198)(189,201)(190,204)(191,203)(192,202)(206,208)
(210,212)(214,216)(217,229)(218,232)(219,231)(220,230)(221,233)(222,236)
(223,235)(224,234)(225,237)(226,240)(227,239)(228,238)(242,244)(246,248)
(250,252)(253,265)(254,268)(255,267)(256,266)(257,269)(258,272)(259,271)
(260,270)(261,273)(262,276)(263,275)(264,274)(278,280)(282,284)(286,288);;
s3 := (  1,146)(  2,145)(  3,147)(  4,148)(  5,150)(  6,149)(  7,151)(  8,152)
(  9,154)( 10,153)( 11,155)( 12,156)( 13,170)( 14,169)( 15,171)( 16,172)
( 17,174)( 18,173)( 19,175)( 20,176)( 21,178)( 22,177)( 23,179)( 24,180)
( 25,158)( 26,157)( 27,159)( 28,160)( 29,162)( 30,161)( 31,163)( 32,164)
( 33,166)( 34,165)( 35,167)( 36,168)( 37,182)( 38,181)( 39,183)( 40,184)
( 41,186)( 42,185)( 43,187)( 44,188)( 45,190)( 46,189)( 47,191)( 48,192)
( 49,206)( 50,205)( 51,207)( 52,208)( 53,210)( 54,209)( 55,211)( 56,212)
( 57,214)( 58,213)( 59,215)( 60,216)( 61,194)( 62,193)( 63,195)( 64,196)
( 65,198)( 66,197)( 67,199)( 68,200)( 69,202)( 70,201)( 71,203)( 72,204)
( 73,218)( 74,217)( 75,219)( 76,220)( 77,222)( 78,221)( 79,223)( 80,224)
( 81,226)( 82,225)( 83,227)( 84,228)( 85,242)( 86,241)( 87,243)( 88,244)
( 89,246)( 90,245)( 91,247)( 92,248)( 93,250)( 94,249)( 95,251)( 96,252)
( 97,230)( 98,229)( 99,231)(100,232)(101,234)(102,233)(103,235)(104,236)
(105,238)(106,237)(107,239)(108,240)(109,254)(110,253)(111,255)(112,256)
(113,258)(114,257)(115,259)(116,260)(117,262)(118,261)(119,263)(120,264)
(121,278)(122,277)(123,279)(124,280)(125,282)(126,281)(127,283)(128,284)
(129,286)(130,285)(131,287)(132,288)(133,266)(134,265)(135,267)(136,268)
(137,270)(138,269)(139,271)(140,272)(141,274)(142,273)(143,275)(144,276);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(288)!(  5,  9)(  6, 10)(  7, 11)(  8, 12)( 17, 21)( 18, 22)( 19, 23)
( 20, 24)( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 41, 45)( 42, 46)( 43, 47)
( 44, 48)( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 65, 69)( 66, 70)( 67, 71)
( 68, 72)( 73,109)( 74,110)( 75,111)( 76,112)( 77,117)( 78,118)( 79,119)
( 80,120)( 81,113)( 82,114)( 83,115)( 84,116)( 85,121)( 86,122)( 87,123)
( 88,124)( 89,129)( 90,130)( 91,131)( 92,132)( 93,125)( 94,126)( 95,127)
( 96,128)( 97,133)( 98,134)( 99,135)(100,136)(101,141)(102,142)(103,143)
(104,144)(105,137)(106,138)(107,139)(108,140)(149,153)(150,154)(151,155)
(152,156)(161,165)(162,166)(163,167)(164,168)(173,177)(174,178)(175,179)
(176,180)(185,189)(186,190)(187,191)(188,192)(197,201)(198,202)(199,203)
(200,204)(209,213)(210,214)(211,215)(212,216)(217,253)(218,254)(219,255)
(220,256)(221,261)(222,262)(223,263)(224,264)(225,257)(226,258)(227,259)
(228,260)(229,265)(230,266)(231,267)(232,268)(233,273)(234,274)(235,275)
(236,276)(237,269)(238,270)(239,271)(240,272)(241,277)(242,278)(243,279)
(244,280)(245,285)(246,286)(247,287)(248,288)(249,281)(250,282)(251,283)
(252,284);
s1 := Sym(288)!(  1, 77)(  2, 78)(  3, 80)(  4, 79)(  5, 73)(  6, 74)(  7, 76)
(  8, 75)(  9, 81)( 10, 82)( 11, 84)( 12, 83)( 13,101)( 14,102)( 15,104)
( 16,103)( 17, 97)( 18, 98)( 19,100)( 20, 99)( 21,105)( 22,106)( 23,108)
( 24,107)( 25, 89)( 26, 90)( 27, 92)( 28, 91)( 29, 85)( 30, 86)( 31, 88)
( 32, 87)( 33, 93)( 34, 94)( 35, 96)( 36, 95)( 37,113)( 38,114)( 39,116)
( 40,115)( 41,109)( 42,110)( 43,112)( 44,111)( 45,117)( 46,118)( 47,120)
( 48,119)( 49,137)( 50,138)( 51,140)( 52,139)( 53,133)( 54,134)( 55,136)
( 56,135)( 57,141)( 58,142)( 59,144)( 60,143)( 61,125)( 62,126)( 63,128)
( 64,127)( 65,121)( 66,122)( 67,124)( 68,123)( 69,129)( 70,130)( 71,132)
( 72,131)(145,221)(146,222)(147,224)(148,223)(149,217)(150,218)(151,220)
(152,219)(153,225)(154,226)(155,228)(156,227)(157,245)(158,246)(159,248)
(160,247)(161,241)(162,242)(163,244)(164,243)(165,249)(166,250)(167,252)
(168,251)(169,233)(170,234)(171,236)(172,235)(173,229)(174,230)(175,232)
(176,231)(177,237)(178,238)(179,240)(180,239)(181,257)(182,258)(183,260)
(184,259)(185,253)(186,254)(187,256)(188,255)(189,261)(190,262)(191,264)
(192,263)(193,281)(194,282)(195,284)(196,283)(197,277)(198,278)(199,280)
(200,279)(201,285)(202,286)(203,288)(204,287)(205,269)(206,270)(207,272)
(208,271)(209,265)(210,266)(211,268)(212,267)(213,273)(214,274)(215,276)
(216,275);
s2 := Sym(288)!(  1, 13)(  2, 16)(  3, 15)(  4, 14)(  5, 17)(  6, 20)(  7, 19)
(  8, 18)(  9, 21)( 10, 24)( 11, 23)( 12, 22)( 26, 28)( 30, 32)( 34, 36)
( 37, 49)( 38, 52)( 39, 51)( 40, 50)( 41, 53)( 42, 56)( 43, 55)( 44, 54)
( 45, 57)( 46, 60)( 47, 59)( 48, 58)( 62, 64)( 66, 68)( 70, 72)( 73, 85)
( 74, 88)( 75, 87)( 76, 86)( 77, 89)( 78, 92)( 79, 91)( 80, 90)( 81, 93)
( 82, 96)( 83, 95)( 84, 94)( 98,100)(102,104)(106,108)(109,121)(110,124)
(111,123)(112,122)(113,125)(114,128)(115,127)(116,126)(117,129)(118,132)
(119,131)(120,130)(134,136)(138,140)(142,144)(145,157)(146,160)(147,159)
(148,158)(149,161)(150,164)(151,163)(152,162)(153,165)(154,168)(155,167)
(156,166)(170,172)(174,176)(178,180)(181,193)(182,196)(183,195)(184,194)
(185,197)(186,200)(187,199)(188,198)(189,201)(190,204)(191,203)(192,202)
(206,208)(210,212)(214,216)(217,229)(218,232)(219,231)(220,230)(221,233)
(222,236)(223,235)(224,234)(225,237)(226,240)(227,239)(228,238)(242,244)
(246,248)(250,252)(253,265)(254,268)(255,267)(256,266)(257,269)(258,272)
(259,271)(260,270)(261,273)(262,276)(263,275)(264,274)(278,280)(282,284)
(286,288);
s3 := Sym(288)!(  1,146)(  2,145)(  3,147)(  4,148)(  5,150)(  6,149)(  7,151)
(  8,152)(  9,154)( 10,153)( 11,155)( 12,156)( 13,170)( 14,169)( 15,171)
( 16,172)( 17,174)( 18,173)( 19,175)( 20,176)( 21,178)( 22,177)( 23,179)
( 24,180)( 25,158)( 26,157)( 27,159)( 28,160)( 29,162)( 30,161)( 31,163)
( 32,164)( 33,166)( 34,165)( 35,167)( 36,168)( 37,182)( 38,181)( 39,183)
( 40,184)( 41,186)( 42,185)( 43,187)( 44,188)( 45,190)( 46,189)( 47,191)
( 48,192)( 49,206)( 50,205)( 51,207)( 52,208)( 53,210)( 54,209)( 55,211)
( 56,212)( 57,214)( 58,213)( 59,215)( 60,216)( 61,194)( 62,193)( 63,195)
( 64,196)( 65,198)( 66,197)( 67,199)( 68,200)( 69,202)( 70,201)( 71,203)
( 72,204)( 73,218)( 74,217)( 75,219)( 76,220)( 77,222)( 78,221)( 79,223)
( 80,224)( 81,226)( 82,225)( 83,227)( 84,228)( 85,242)( 86,241)( 87,243)
( 88,244)( 89,246)( 90,245)( 91,247)( 92,248)( 93,250)( 94,249)( 95,251)
( 96,252)( 97,230)( 98,229)( 99,231)(100,232)(101,234)(102,233)(103,235)
(104,236)(105,238)(106,237)(107,239)(108,240)(109,254)(110,253)(111,255)
(112,256)(113,258)(114,257)(115,259)(116,260)(117,262)(118,261)(119,263)
(120,264)(121,278)(122,277)(123,279)(124,280)(125,282)(126,281)(127,283)
(128,284)(129,286)(130,285)(131,287)(132,288)(133,266)(134,265)(135,267)
(136,268)(137,270)(138,269)(139,271)(140,272)(141,274)(142,273)(143,275)
(144,276);
poly := sub<Sym(288)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*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 >; 
 
References : None.
to this polytope