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Polytope of Type {4,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,6}*1152f
if this polytope has a name.
Group : SmallGroup(1152,157640)
Rank : 4
Schlafli Type : {4,6,6}
Number of vertices, edges, etc : 4, 48, 72, 24
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 : {4,6,3}*576a, {2,6,6}*576a
   3-fold quotients : {4,6,6}*384
   4-fold quotients : {4,6,6}*288c, {2,6,3}*288
   6-fold quotients : {4,6,3}*192, {2,6,6}*192
   8-fold quotients : {4,6,3}*144, {2,6,6}*144b
   12-fold quotients : {4,2,6}*96, {2,3,6}*96, {2,6,3}*96
   16-fold quotients : {2,6,3}*72
   24-fold quotients : {4,2,3}*48, {2,3,3}*48, {2,2,6}*48
   36-fold quotients : {4,2,2}*32
   48-fold quotients : {2,2,3}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1, 73)(  2, 74)(  3, 75)(  4, 76)(  5, 77)(  6, 78)(  7, 79)(  8, 80)
(  9, 81)( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)
( 17, 89)( 18, 90)( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)( 24, 96)
( 25, 97)( 26, 98)( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)( 32,104)
( 33,105)( 34,106)( 35,107)( 36,108)( 37,109)( 38,110)( 39,111)( 40,112)
( 41,113)( 42,114)( 43,115)( 44,116)( 45,117)( 46,118)( 47,119)( 48,120)
( 49,121)( 50,122)( 51,123)( 52,124)( 53,125)( 54,126)( 55,127)( 56,128)
( 57,129)( 58,130)( 59,131)( 60,132)( 61,133)( 62,134)( 63,135)( 64,136)
( 65,137)( 66,138)( 67,139)( 68,140)( 69,141)( 70,142)( 71,143)( 72,144)
(145,217)(146,218)(147,219)(148,220)(149,221)(150,222)(151,223)(152,224)
(153,225)(154,226)(155,227)(156,228)(157,229)(158,230)(159,231)(160,232)
(161,233)(162,234)(163,235)(164,236)(165,237)(166,238)(167,239)(168,240)
(169,241)(170,242)(171,243)(172,244)(173,245)(174,246)(175,247)(176,248)
(177,249)(178,250)(179,251)(180,252)(181,253)(182,254)(183,255)(184,256)
(185,257)(186,258)(187,259)(188,260)(189,261)(190,262)(191,263)(192,264)
(193,265)(194,266)(195,267)(196,268)(197,269)(198,270)(199,271)(200,272)
(201,273)(202,274)(203,275)(204,276)(205,277)(206,278)(207,279)(208,280)
(209,281)(210,282)(211,283)(212,284)(213,285)(214,286)(215,287)(216,288);;
s1 := (  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);;
s2 := (  1, 13)(  2, 16)(  3, 15)(  4, 14)(  5, 21)(  6, 24)(  7, 23)(  8, 22)
(  9, 17)( 10, 20)( 11, 19)( 12, 18)( 26, 28)( 29, 33)( 30, 36)( 31, 35)
( 32, 34)( 37, 49)( 38, 52)( 39, 51)( 40, 50)( 41, 57)( 42, 60)( 43, 59)
( 44, 58)( 45, 53)( 46, 56)( 47, 55)( 48, 54)( 62, 64)( 65, 69)( 66, 72)
( 67, 71)( 68, 70)( 73, 85)( 74, 88)( 75, 87)( 76, 86)( 77, 93)( 78, 96)
( 79, 95)( 80, 94)( 81, 89)( 82, 92)( 83, 91)( 84, 90)( 98,100)(101,105)
(102,108)(103,107)(104,106)(109,121)(110,124)(111,123)(112,122)(113,129)
(114,132)(115,131)(116,130)(117,125)(118,128)(119,127)(120,126)(134,136)
(137,141)(138,144)(139,143)(140,142)(145,157)(146,160)(147,159)(148,158)
(149,165)(150,168)(151,167)(152,166)(153,161)(154,164)(155,163)(156,162)
(170,172)(173,177)(174,180)(175,179)(176,178)(181,193)(182,196)(183,195)
(184,194)(185,201)(186,204)(187,203)(188,202)(189,197)(190,200)(191,199)
(192,198)(206,208)(209,213)(210,216)(211,215)(212,214)(217,229)(218,232)
(219,231)(220,230)(221,237)(222,240)(223,239)(224,238)(225,233)(226,236)
(227,235)(228,234)(242,244)(245,249)(246,252)(247,251)(248,250)(253,265)
(254,268)(255,267)(256,266)(257,273)(258,276)(259,275)(260,274)(261,269)
(262,272)(263,271)(264,270)(278,280)(281,285)(282,288)(283,287)(284,286);;
s3 := (  1,150)(  2,149)(  3,151)(  4,152)(  5,146)(  6,145)(  7,147)(  8,148)
(  9,154)( 10,153)( 11,155)( 12,156)( 13,174)( 14,173)( 15,175)( 16,176)
( 17,170)( 18,169)( 19,171)( 20,172)( 21,178)( 22,177)( 23,179)( 24,180)
( 25,162)( 26,161)( 27,163)( 28,164)( 29,158)( 30,157)( 31,159)( 32,160)
( 33,166)( 34,165)( 35,167)( 36,168)( 37,186)( 38,185)( 39,187)( 40,188)
( 41,182)( 42,181)( 43,183)( 44,184)( 45,190)( 46,189)( 47,191)( 48,192)
( 49,210)( 50,209)( 51,211)( 52,212)( 53,206)( 54,205)( 55,207)( 56,208)
( 57,214)( 58,213)( 59,215)( 60,216)( 61,198)( 62,197)( 63,199)( 64,200)
( 65,194)( 66,193)( 67,195)( 68,196)( 69,202)( 70,201)( 71,203)( 72,204)
( 73,222)( 74,221)( 75,223)( 76,224)( 77,218)( 78,217)( 79,219)( 80,220)
( 81,226)( 82,225)( 83,227)( 84,228)( 85,246)( 86,245)( 87,247)( 88,248)
( 89,242)( 90,241)( 91,243)( 92,244)( 93,250)( 94,249)( 95,251)( 96,252)
( 97,234)( 98,233)( 99,235)(100,236)(101,230)(102,229)(103,231)(104,232)
(105,238)(106,237)(107,239)(108,240)(109,258)(110,257)(111,259)(112,260)
(113,254)(114,253)(115,255)(116,256)(117,262)(118,261)(119,263)(120,264)
(121,282)(122,281)(123,283)(124,284)(125,278)(126,277)(127,279)(128,280)
(129,286)(130,285)(131,287)(132,288)(133,270)(134,269)(135,271)(136,272)
(137,266)(138,265)(139,267)(140,268)(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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(288)!(  1, 73)(  2, 74)(  3, 75)(  4, 76)(  5, 77)(  6, 78)(  7, 79)
(  8, 80)(  9, 81)( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)
( 16, 88)( 17, 89)( 18, 90)( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)
( 24, 96)( 25, 97)( 26, 98)( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)
( 32,104)( 33,105)( 34,106)( 35,107)( 36,108)( 37,109)( 38,110)( 39,111)
( 40,112)( 41,113)( 42,114)( 43,115)( 44,116)( 45,117)( 46,118)( 47,119)
( 48,120)( 49,121)( 50,122)( 51,123)( 52,124)( 53,125)( 54,126)( 55,127)
( 56,128)( 57,129)( 58,130)( 59,131)( 60,132)( 61,133)( 62,134)( 63,135)
( 64,136)( 65,137)( 66,138)( 67,139)( 68,140)( 69,141)( 70,142)( 71,143)
( 72,144)(145,217)(146,218)(147,219)(148,220)(149,221)(150,222)(151,223)
(152,224)(153,225)(154,226)(155,227)(156,228)(157,229)(158,230)(159,231)
(160,232)(161,233)(162,234)(163,235)(164,236)(165,237)(166,238)(167,239)
(168,240)(169,241)(170,242)(171,243)(172,244)(173,245)(174,246)(175,247)
(176,248)(177,249)(178,250)(179,251)(180,252)(181,253)(182,254)(183,255)
(184,256)(185,257)(186,258)(187,259)(188,260)(189,261)(190,262)(191,263)
(192,264)(193,265)(194,266)(195,267)(196,268)(197,269)(198,270)(199,271)
(200,272)(201,273)(202,274)(203,275)(204,276)(205,277)(206,278)(207,279)
(208,280)(209,281)(210,282)(211,283)(212,284)(213,285)(214,286)(215,287)
(216,288);
s1 := 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);
s2 := Sym(288)!(  1, 13)(  2, 16)(  3, 15)(  4, 14)(  5, 21)(  6, 24)(  7, 23)
(  8, 22)(  9, 17)( 10, 20)( 11, 19)( 12, 18)( 26, 28)( 29, 33)( 30, 36)
( 31, 35)( 32, 34)( 37, 49)( 38, 52)( 39, 51)( 40, 50)( 41, 57)( 42, 60)
( 43, 59)( 44, 58)( 45, 53)( 46, 56)( 47, 55)( 48, 54)( 62, 64)( 65, 69)
( 66, 72)( 67, 71)( 68, 70)( 73, 85)( 74, 88)( 75, 87)( 76, 86)( 77, 93)
( 78, 96)( 79, 95)( 80, 94)( 81, 89)( 82, 92)( 83, 91)( 84, 90)( 98,100)
(101,105)(102,108)(103,107)(104,106)(109,121)(110,124)(111,123)(112,122)
(113,129)(114,132)(115,131)(116,130)(117,125)(118,128)(119,127)(120,126)
(134,136)(137,141)(138,144)(139,143)(140,142)(145,157)(146,160)(147,159)
(148,158)(149,165)(150,168)(151,167)(152,166)(153,161)(154,164)(155,163)
(156,162)(170,172)(173,177)(174,180)(175,179)(176,178)(181,193)(182,196)
(183,195)(184,194)(185,201)(186,204)(187,203)(188,202)(189,197)(190,200)
(191,199)(192,198)(206,208)(209,213)(210,216)(211,215)(212,214)(217,229)
(218,232)(219,231)(220,230)(221,237)(222,240)(223,239)(224,238)(225,233)
(226,236)(227,235)(228,234)(242,244)(245,249)(246,252)(247,251)(248,250)
(253,265)(254,268)(255,267)(256,266)(257,273)(258,276)(259,275)(260,274)
(261,269)(262,272)(263,271)(264,270)(278,280)(281,285)(282,288)(283,287)
(284,286);
s3 := Sym(288)!(  1,150)(  2,149)(  3,151)(  4,152)(  5,146)(  6,145)(  7,147)
(  8,148)(  9,154)( 10,153)( 11,155)( 12,156)( 13,174)( 14,173)( 15,175)
( 16,176)( 17,170)( 18,169)( 19,171)( 20,172)( 21,178)( 22,177)( 23,179)
( 24,180)( 25,162)( 26,161)( 27,163)( 28,164)( 29,158)( 30,157)( 31,159)
( 32,160)( 33,166)( 34,165)( 35,167)( 36,168)( 37,186)( 38,185)( 39,187)
( 40,188)( 41,182)( 42,181)( 43,183)( 44,184)( 45,190)( 46,189)( 47,191)
( 48,192)( 49,210)( 50,209)( 51,211)( 52,212)( 53,206)( 54,205)( 55,207)
( 56,208)( 57,214)( 58,213)( 59,215)( 60,216)( 61,198)( 62,197)( 63,199)
( 64,200)( 65,194)( 66,193)( 67,195)( 68,196)( 69,202)( 70,201)( 71,203)
( 72,204)( 73,222)( 74,221)( 75,223)( 76,224)( 77,218)( 78,217)( 79,219)
( 80,220)( 81,226)( 82,225)( 83,227)( 84,228)( 85,246)( 86,245)( 87,247)
( 88,248)( 89,242)( 90,241)( 91,243)( 92,244)( 93,250)( 94,249)( 95,251)
( 96,252)( 97,234)( 98,233)( 99,235)(100,236)(101,230)(102,229)(103,231)
(104,232)(105,238)(106,237)(107,239)(108,240)(109,258)(110,257)(111,259)
(112,260)(113,254)(114,253)(115,255)(116,256)(117,262)(118,261)(119,263)
(120,264)(121,282)(122,281)(123,283)(124,284)(125,278)(126,277)(127,279)
(128,280)(129,286)(130,285)(131,287)(132,288)(133,270)(134,269)(135,271)
(136,272)(137,266)(138,265)(139,267)(140,268)(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*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 >; 
 
References : None.
to this polytope