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Polytope of Type {8,6,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6,3}*1152
if this polytope has a name.
Group : SmallGroup(1152,156074)
Rank : 4
Schlafli Type : {8,6,3}
Number of vertices, edges, etc : 8, 96, 36, 12
Order of s0s1s2s3 : 24
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
   3-fold quotients : {8,6,3}*384
   4-fold quotients : {8,6,3}*288, {2,6,3}*288
   6-fold quotients : {4,6,3}*192
   8-fold quotients : {4,6,3}*144
   12-fold quotients : {8,2,3}*96, {2,6,3}*96
   16-fold quotients : {2,6,3}*72
   24-fold quotients : {4,2,3}*48, {2,3,3}*48
   48-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,145)(  2,146)(  3,147)(  4,148)(  5,149)(  6,150)(  7,151)(  8,152)
(  9,153)( 10,154)( 11,155)( 12,156)( 13,157)( 14,158)( 15,159)( 16,160)
( 17,161)( 18,162)( 19,163)( 20,164)( 21,165)( 22,166)( 23,167)( 24,168)
( 25,169)( 26,170)( 27,171)( 28,172)( 29,173)( 30,174)( 31,175)( 32,176)
( 33,177)( 34,178)( 35,179)( 36,180)( 37,181)( 38,182)( 39,183)( 40,184)
( 41,185)( 42,186)( 43,187)( 44,188)( 45,189)( 46,190)( 47,191)( 48,192)
( 49,193)( 50,194)( 51,195)( 52,196)( 53,197)( 54,198)( 55,199)( 56,200)
( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)( 64,208)
( 65,209)( 66,210)( 67,211)( 68,212)( 69,213)( 70,214)( 71,215)( 72,216)
( 73,253)( 74,254)( 75,255)( 76,256)( 77,257)( 78,258)( 79,259)( 80,260)
( 81,261)( 82,262)( 83,263)( 84,264)( 85,265)( 86,266)( 87,267)( 88,268)
( 89,269)( 90,270)( 91,271)( 92,272)( 93,273)( 94,274)( 95,275)( 96,276)
( 97,277)( 98,278)( 99,279)(100,280)(101,281)(102,282)(103,283)(104,284)
(105,285)(106,286)(107,287)(108,288)(109,217)(110,218)(111,219)(112,220)
(113,221)(114,222)(115,223)(116,224)(117,225)(118,226)(119,227)(120,228)
(121,229)(122,230)(123,231)(124,232)(125,233)(126,234)(127,235)(128,236)
(129,237)(130,238)(131,239)(132,240)(133,241)(134,242)(135,243)(136,244)
(137,245)(138,246)(139,247)(140,248)(141,249)(142,250)(143,251)(144,252);;
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)(145,217)(146,218)(147,220)(148,219)(149,221)(150,222)
(151,224)(152,223)(153,225)(154,226)(155,228)(156,227)(157,241)(158,242)
(159,244)(160,243)(161,245)(162,246)(163,248)(164,247)(165,249)(166,250)
(167,252)(168,251)(169,229)(170,230)(171,232)(172,231)(173,233)(174,234)
(175,236)(176,235)(177,237)(178,238)(179,240)(180,239)(181,253)(182,254)
(183,256)(184,255)(185,257)(186,258)(187,260)(188,259)(189,261)(190,262)
(191,264)(192,263)(193,277)(194,278)(195,280)(196,279)(197,281)(198,282)
(199,284)(200,283)(201,285)(202,286)(203,288)(204,287)(205,265)(206,266)
(207,268)(208,267)(209,269)(210,270)(211,272)(212,271)(213,273)(214,274)
(215,276)(216,275);;
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,  6)(  2,  5)(  3,  7)(  4,  8)(  9, 10)( 13, 30)( 14, 29)( 15, 31)
( 16, 32)( 17, 26)( 18, 25)( 19, 27)( 20, 28)( 21, 34)( 22, 33)( 23, 35)
( 24, 36)( 37, 42)( 38, 41)( 39, 43)( 40, 44)( 45, 46)( 49, 66)( 50, 65)
( 51, 67)( 52, 68)( 53, 62)( 54, 61)( 55, 63)( 56, 64)( 57, 70)( 58, 69)
( 59, 71)( 60, 72)( 73, 78)( 74, 77)( 75, 79)( 76, 80)( 81, 82)( 85,102)
( 86,101)( 87,103)( 88,104)( 89, 98)( 90, 97)( 91, 99)( 92,100)( 93,106)
( 94,105)( 95,107)( 96,108)(109,114)(110,113)(111,115)(112,116)(117,118)
(121,138)(122,137)(123,139)(124,140)(125,134)(126,133)(127,135)(128,136)
(129,142)(130,141)(131,143)(132,144)(145,150)(146,149)(147,151)(148,152)
(153,154)(157,174)(158,173)(159,175)(160,176)(161,170)(162,169)(163,171)
(164,172)(165,178)(166,177)(167,179)(168,180)(181,186)(182,185)(183,187)
(184,188)(189,190)(193,210)(194,209)(195,211)(196,212)(197,206)(198,205)
(199,207)(200,208)(201,214)(202,213)(203,215)(204,216)(217,222)(218,221)
(219,223)(220,224)(225,226)(229,246)(230,245)(231,247)(232,248)(233,242)
(234,241)(235,243)(236,244)(237,250)(238,249)(239,251)(240,252)(253,258)
(254,257)(255,259)(256,260)(261,262)(265,282)(266,281)(267,283)(268,284)
(269,278)(270,277)(271,279)(272,280)(273,286)(274,285)(275,287)(276,288);;
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, s2*s3*s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, 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, 
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)!(  1,145)(  2,146)(  3,147)(  4,148)(  5,149)(  6,150)(  7,151)
(  8,152)(  9,153)( 10,154)( 11,155)( 12,156)( 13,157)( 14,158)( 15,159)
( 16,160)( 17,161)( 18,162)( 19,163)( 20,164)( 21,165)( 22,166)( 23,167)
( 24,168)( 25,169)( 26,170)( 27,171)( 28,172)( 29,173)( 30,174)( 31,175)
( 32,176)( 33,177)( 34,178)( 35,179)( 36,180)( 37,181)( 38,182)( 39,183)
( 40,184)( 41,185)( 42,186)( 43,187)( 44,188)( 45,189)( 46,190)( 47,191)
( 48,192)( 49,193)( 50,194)( 51,195)( 52,196)( 53,197)( 54,198)( 55,199)
( 56,200)( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)
( 64,208)( 65,209)( 66,210)( 67,211)( 68,212)( 69,213)( 70,214)( 71,215)
( 72,216)( 73,253)( 74,254)( 75,255)( 76,256)( 77,257)( 78,258)( 79,259)
( 80,260)( 81,261)( 82,262)( 83,263)( 84,264)( 85,265)( 86,266)( 87,267)
( 88,268)( 89,269)( 90,270)( 91,271)( 92,272)( 93,273)( 94,274)( 95,275)
( 96,276)( 97,277)( 98,278)( 99,279)(100,280)(101,281)(102,282)(103,283)
(104,284)(105,285)(106,286)(107,287)(108,288)(109,217)(110,218)(111,219)
(112,220)(113,221)(114,222)(115,223)(116,224)(117,225)(118,226)(119,227)
(120,228)(121,229)(122,230)(123,231)(124,232)(125,233)(126,234)(127,235)
(128,236)(129,237)(130,238)(131,239)(132,240)(133,241)(134,242)(135,243)
(136,244)(137,245)(138,246)(139,247)(140,248)(141,249)(142,250)(143,251)
(144,252);
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)(145,217)(146,218)(147,220)(148,219)(149,221)
(150,222)(151,224)(152,223)(153,225)(154,226)(155,228)(156,227)(157,241)
(158,242)(159,244)(160,243)(161,245)(162,246)(163,248)(164,247)(165,249)
(166,250)(167,252)(168,251)(169,229)(170,230)(171,232)(172,231)(173,233)
(174,234)(175,236)(176,235)(177,237)(178,238)(179,240)(180,239)(181,253)
(182,254)(183,256)(184,255)(185,257)(186,258)(187,260)(188,259)(189,261)
(190,262)(191,264)(192,263)(193,277)(194,278)(195,280)(196,279)(197,281)
(198,282)(199,284)(200,283)(201,285)(202,286)(203,288)(204,287)(205,265)
(206,266)(207,268)(208,267)(209,269)(210,270)(211,272)(212,271)(213,273)
(214,274)(215,276)(216,275);
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,  6)(  2,  5)(  3,  7)(  4,  8)(  9, 10)( 13, 30)( 14, 29)
( 15, 31)( 16, 32)( 17, 26)( 18, 25)( 19, 27)( 20, 28)( 21, 34)( 22, 33)
( 23, 35)( 24, 36)( 37, 42)( 38, 41)( 39, 43)( 40, 44)( 45, 46)( 49, 66)
( 50, 65)( 51, 67)( 52, 68)( 53, 62)( 54, 61)( 55, 63)( 56, 64)( 57, 70)
( 58, 69)( 59, 71)( 60, 72)( 73, 78)( 74, 77)( 75, 79)( 76, 80)( 81, 82)
( 85,102)( 86,101)( 87,103)( 88,104)( 89, 98)( 90, 97)( 91, 99)( 92,100)
( 93,106)( 94,105)( 95,107)( 96,108)(109,114)(110,113)(111,115)(112,116)
(117,118)(121,138)(122,137)(123,139)(124,140)(125,134)(126,133)(127,135)
(128,136)(129,142)(130,141)(131,143)(132,144)(145,150)(146,149)(147,151)
(148,152)(153,154)(157,174)(158,173)(159,175)(160,176)(161,170)(162,169)
(163,171)(164,172)(165,178)(166,177)(167,179)(168,180)(181,186)(182,185)
(183,187)(184,188)(189,190)(193,210)(194,209)(195,211)(196,212)(197,206)
(198,205)(199,207)(200,208)(201,214)(202,213)(203,215)(204,216)(217,222)
(218,221)(219,223)(220,224)(225,226)(229,246)(230,245)(231,247)(232,248)
(233,242)(234,241)(235,243)(236,244)(237,250)(238,249)(239,251)(240,252)
(253,258)(254,257)(255,259)(256,260)(261,262)(265,282)(266,281)(267,283)
(268,284)(269,278)(270,277)(271,279)(272,280)(273,286)(274,285)(275,287)
(276,288);
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, 
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
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, 
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