Polytope of Type {12,4,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4,6}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157549)
Rank : 4
Schlafli Type : {12,4,6}
Number of vertices, edges, etc : 24, 48, 24, 6
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 : {6,4,6}*576b
   3-fold quotients : {12,4,2}*384b
   4-fold quotients : {12,2,6}*288, {3,4,6}*288
   6-fold quotients : {12,4,2}*192b, {12,4,2}*192c, {6,4,2}*192
   8-fold quotients : {12,2,3}*144, {6,2,6}*144
   12-fold quotients : {12,2,2}*96, {4,2,6}*96, {3,4,2}*96, {6,4,2}*96b, {6,4,2}*96c
   16-fold quotients : {3,2,6}*72, {6,2,3}*72
   24-fold quotients : {4,2,3}*48, {3,4,2}*48, {2,2,6}*48, {6,2,2}*48
   32-fold quotients : {3,2,3}*36
   36-fold quotients : {4,2,2}*32
   48-fold quotients : {2,2,3}*24, {3,2,2}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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