Polytope of Type {6,4,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,3}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157852)
Rank : 4
Schlafli Type : {6,4,3}
Number of vertices, edges, etc : 24, 96, 48, 12
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 4
Special Properties :
Orientable
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 : {3,4,3}*576
16-fold quotients : {6,2,3}*72
32-fold quotients : {3,2,3}*36
48-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 5)( 3, 9)( 4, 13)( 7, 10)( 8, 14)( 12, 15)( 17, 33)( 18, 37)
( 19, 41)( 20, 45)( 21, 34)( 22, 38)( 23, 42)( 24, 46)( 25, 35)( 26, 39)
( 27, 43)( 28, 47)( 29, 36)( 30, 40)( 31, 44)( 32, 48)( 49, 65)( 50, 69)
( 51, 73)( 52, 77)( 53, 66)( 54, 70)( 55, 74)( 56, 78)( 57, 67)( 58, 71)
( 59, 75)( 60, 79)( 61, 68)( 62, 72)( 63, 76)( 64, 80)( 82, 85)( 83, 89)
( 84, 93)( 87, 90)( 88, 94)( 92, 95)( 97,129)( 98,133)( 99,137)(100,141)
(101,130)(102,134)(103,138)(104,142)(105,131)(106,135)(107,139)(108,143)
(109,132)(110,136)(111,140)(112,144)(114,117)(115,121)(116,125)(119,122)
(120,126)(124,127)(146,149)(147,153)(148,157)(151,154)(152,158)(156,159)
(161,177)(162,181)(163,185)(164,189)(165,178)(166,182)(167,186)(168,190)
(169,179)(170,183)(171,187)(172,191)(173,180)(174,184)(175,188)(176,192)
(193,209)(194,213)(195,217)(196,221)(197,210)(198,214)(199,218)(200,222)
(201,211)(202,215)(203,219)(204,223)(205,212)(206,216)(207,220)(208,224)
(226,229)(227,233)(228,237)(231,234)(232,238)(236,239)(241,273)(242,277)
(243,281)(244,285)(245,274)(246,278)(247,282)(248,286)(249,275)(250,279)
(251,283)(252,287)(253,276)(254,280)(255,284)(256,288)(258,261)(259,265)
(260,269)(263,266)(264,270)(268,271);;
s1 := ( 1,161)( 2,169)( 3,173)( 4,165)( 5,164)( 6,172)( 7,176)( 8,168)
( 9,162)( 10,170)( 11,174)( 12,166)( 13,163)( 14,171)( 15,175)( 16,167)
( 17,145)( 18,153)( 19,157)( 20,149)( 21,148)( 22,156)( 23,160)( 24,152)
( 25,146)( 26,154)( 27,158)( 28,150)( 29,147)( 30,155)( 31,159)( 32,151)
( 33,177)( 34,185)( 35,189)( 36,181)( 37,180)( 38,188)( 39,192)( 40,184)
( 41,178)( 42,186)( 43,190)( 44,182)( 45,179)( 46,187)( 47,191)( 48,183)
( 49,225)( 50,233)( 51,237)( 52,229)( 53,228)( 54,236)( 55,240)( 56,232)
( 57,226)( 58,234)( 59,238)( 60,230)( 61,227)( 62,235)( 63,239)( 64,231)
( 65,209)( 66,217)( 67,221)( 68,213)( 69,212)( 70,220)( 71,224)( 72,216)
( 73,210)( 74,218)( 75,222)( 76,214)( 77,211)( 78,219)( 79,223)( 80,215)
( 81,193)( 82,201)( 83,205)( 84,197)( 85,196)( 86,204)( 87,208)( 88,200)
( 89,194)( 90,202)( 91,206)( 92,198)( 93,195)( 94,203)( 95,207)( 96,199)
( 97,241)( 98,249)( 99,253)(100,245)(101,244)(102,252)(103,256)(104,248)
(105,242)(106,250)(107,254)(108,246)(109,243)(110,251)(111,255)(112,247)
(113,273)(114,281)(115,285)(116,277)(117,276)(118,284)(119,288)(120,280)
(121,274)(122,282)(123,286)(124,278)(125,275)(126,283)(127,287)(128,279)
(129,257)(130,265)(131,269)(132,261)(133,260)(134,268)(135,272)(136,264)
(137,258)(138,266)(139,270)(140,262)(141,259)(142,267)(143,271)(144,263);;
s2 := ( 1, 6)( 3, 10)( 4, 14)( 7, 9)( 8, 13)( 12, 15)( 17, 22)( 19, 26)
( 20, 30)( 23, 25)( 24, 29)( 28, 31)( 33, 38)( 35, 42)( 36, 46)( 39, 41)
( 40, 45)( 44, 47)( 49,134)( 50,130)( 51,138)( 52,142)( 53,133)( 54,129)
( 55,137)( 56,141)( 57,135)( 58,131)( 59,139)( 60,143)( 61,136)( 62,132)
( 63,140)( 64,144)( 65,102)( 66, 98)( 67,106)( 68,110)( 69,101)( 70, 97)
( 71,105)( 72,109)( 73,103)( 74, 99)( 75,107)( 76,111)( 77,104)( 78,100)
( 79,108)( 80,112)( 81,118)( 82,114)( 83,122)( 84,126)( 85,117)( 86,113)
( 87,121)( 88,125)( 89,119)( 90,115)( 91,123)( 92,127)( 93,120)( 94,116)
( 95,124)( 96,128)(145,150)(147,154)(148,158)(151,153)(152,157)(156,159)
(161,166)(163,170)(164,174)(167,169)(168,173)(172,175)(177,182)(179,186)
(180,190)(183,185)(184,189)(188,191)(193,278)(194,274)(195,282)(196,286)
(197,277)(198,273)(199,281)(200,285)(201,279)(202,275)(203,283)(204,287)
(205,280)(206,276)(207,284)(208,288)(209,246)(210,242)(211,250)(212,254)
(213,245)(214,241)(215,249)(216,253)(217,247)(218,243)(219,251)(220,255)
(221,248)(222,244)(223,252)(224,256)(225,262)(226,258)(227,266)(228,270)
(229,261)(230,257)(231,265)(232,269)(233,263)(234,259)(235,267)(236,271)
(237,264)(238,260)(239,268)(240,272);;
s3 := ( 1,113)( 2,125)( 3,121)( 4,117)( 5,116)( 6,128)( 7,124)( 8,120)
( 9,115)( 10,127)( 11,123)( 12,119)( 13,114)( 14,126)( 15,122)( 16,118)
( 17,129)( 18,141)( 19,137)( 20,133)( 21,132)( 22,144)( 23,140)( 24,136)
( 25,131)( 26,143)( 27,139)( 28,135)( 29,130)( 30,142)( 31,138)( 32,134)
( 33, 97)( 34,109)( 35,105)( 36,101)( 37,100)( 38,112)( 39,108)( 40,104)
( 41, 99)( 42,111)( 43,107)( 44,103)( 45, 98)( 46,110)( 47,106)( 48,102)
( 50, 61)( 51, 57)( 52, 53)( 54, 64)( 55, 60)( 58, 63)( 66, 77)( 67, 73)
( 68, 69)( 70, 80)( 71, 76)( 74, 79)( 82, 93)( 83, 89)( 84, 85)( 86, 96)
( 87, 92)( 90, 95)(145,257)(146,269)(147,265)(148,261)(149,260)(150,272)
(151,268)(152,264)(153,259)(154,271)(155,267)(156,263)(157,258)(158,270)
(159,266)(160,262)(161,273)(162,285)(163,281)(164,277)(165,276)(166,288)
(167,284)(168,280)(169,275)(170,287)(171,283)(172,279)(173,274)(174,286)
(175,282)(176,278)(177,241)(178,253)(179,249)(180,245)(181,244)(182,256)
(183,252)(184,248)(185,243)(186,255)(187,251)(188,247)(189,242)(190,254)
(191,250)(192,246)(194,205)(195,201)(196,197)(198,208)(199,204)(202,207)
(210,221)(211,217)(212,213)(214,224)(215,220)(218,223)(226,237)(227,233)
(228,229)(230,240)(231,236)(234,239);;
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,
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s3*s2*s1*s2*s0*s1*s2*s0*s3*s2*s1*s2*s0*s1*s3*s2*s3*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(288)!( 2, 5)( 3, 9)( 4, 13)( 7, 10)( 8, 14)( 12, 15)( 17, 33)
( 18, 37)( 19, 41)( 20, 45)( 21, 34)( 22, 38)( 23, 42)( 24, 46)( 25, 35)
( 26, 39)( 27, 43)( 28, 47)( 29, 36)( 30, 40)( 31, 44)( 32, 48)( 49, 65)
( 50, 69)( 51, 73)( 52, 77)( 53, 66)( 54, 70)( 55, 74)( 56, 78)( 57, 67)
( 58, 71)( 59, 75)( 60, 79)( 61, 68)( 62, 72)( 63, 76)( 64, 80)( 82, 85)
( 83, 89)( 84, 93)( 87, 90)( 88, 94)( 92, 95)( 97,129)( 98,133)( 99,137)
(100,141)(101,130)(102,134)(103,138)(104,142)(105,131)(106,135)(107,139)
(108,143)(109,132)(110,136)(111,140)(112,144)(114,117)(115,121)(116,125)
(119,122)(120,126)(124,127)(146,149)(147,153)(148,157)(151,154)(152,158)
(156,159)(161,177)(162,181)(163,185)(164,189)(165,178)(166,182)(167,186)
(168,190)(169,179)(170,183)(171,187)(172,191)(173,180)(174,184)(175,188)
(176,192)(193,209)(194,213)(195,217)(196,221)(197,210)(198,214)(199,218)
(200,222)(201,211)(202,215)(203,219)(204,223)(205,212)(206,216)(207,220)
(208,224)(226,229)(227,233)(228,237)(231,234)(232,238)(236,239)(241,273)
(242,277)(243,281)(244,285)(245,274)(246,278)(247,282)(248,286)(249,275)
(250,279)(251,283)(252,287)(253,276)(254,280)(255,284)(256,288)(258,261)
(259,265)(260,269)(263,266)(264,270)(268,271);
s1 := Sym(288)!( 1,161)( 2,169)( 3,173)( 4,165)( 5,164)( 6,172)( 7,176)
( 8,168)( 9,162)( 10,170)( 11,174)( 12,166)( 13,163)( 14,171)( 15,175)
( 16,167)( 17,145)( 18,153)( 19,157)( 20,149)( 21,148)( 22,156)( 23,160)
( 24,152)( 25,146)( 26,154)( 27,158)( 28,150)( 29,147)( 30,155)( 31,159)
( 32,151)( 33,177)( 34,185)( 35,189)( 36,181)( 37,180)( 38,188)( 39,192)
( 40,184)( 41,178)( 42,186)( 43,190)( 44,182)( 45,179)( 46,187)( 47,191)
( 48,183)( 49,225)( 50,233)( 51,237)( 52,229)( 53,228)( 54,236)( 55,240)
( 56,232)( 57,226)( 58,234)( 59,238)( 60,230)( 61,227)( 62,235)( 63,239)
( 64,231)( 65,209)( 66,217)( 67,221)( 68,213)( 69,212)( 70,220)( 71,224)
( 72,216)( 73,210)( 74,218)( 75,222)( 76,214)( 77,211)( 78,219)( 79,223)
( 80,215)( 81,193)( 82,201)( 83,205)( 84,197)( 85,196)( 86,204)( 87,208)
( 88,200)( 89,194)( 90,202)( 91,206)( 92,198)( 93,195)( 94,203)( 95,207)
( 96,199)( 97,241)( 98,249)( 99,253)(100,245)(101,244)(102,252)(103,256)
(104,248)(105,242)(106,250)(107,254)(108,246)(109,243)(110,251)(111,255)
(112,247)(113,273)(114,281)(115,285)(116,277)(117,276)(118,284)(119,288)
(120,280)(121,274)(122,282)(123,286)(124,278)(125,275)(126,283)(127,287)
(128,279)(129,257)(130,265)(131,269)(132,261)(133,260)(134,268)(135,272)
(136,264)(137,258)(138,266)(139,270)(140,262)(141,259)(142,267)(143,271)
(144,263);
s2 := Sym(288)!( 1, 6)( 3, 10)( 4, 14)( 7, 9)( 8, 13)( 12, 15)( 17, 22)
( 19, 26)( 20, 30)( 23, 25)( 24, 29)( 28, 31)( 33, 38)( 35, 42)( 36, 46)
( 39, 41)( 40, 45)( 44, 47)( 49,134)( 50,130)( 51,138)( 52,142)( 53,133)
( 54,129)( 55,137)( 56,141)( 57,135)( 58,131)( 59,139)( 60,143)( 61,136)
( 62,132)( 63,140)( 64,144)( 65,102)( 66, 98)( 67,106)( 68,110)( 69,101)
( 70, 97)( 71,105)( 72,109)( 73,103)( 74, 99)( 75,107)( 76,111)( 77,104)
( 78,100)( 79,108)( 80,112)( 81,118)( 82,114)( 83,122)( 84,126)( 85,117)
( 86,113)( 87,121)( 88,125)( 89,119)( 90,115)( 91,123)( 92,127)( 93,120)
( 94,116)( 95,124)( 96,128)(145,150)(147,154)(148,158)(151,153)(152,157)
(156,159)(161,166)(163,170)(164,174)(167,169)(168,173)(172,175)(177,182)
(179,186)(180,190)(183,185)(184,189)(188,191)(193,278)(194,274)(195,282)
(196,286)(197,277)(198,273)(199,281)(200,285)(201,279)(202,275)(203,283)
(204,287)(205,280)(206,276)(207,284)(208,288)(209,246)(210,242)(211,250)
(212,254)(213,245)(214,241)(215,249)(216,253)(217,247)(218,243)(219,251)
(220,255)(221,248)(222,244)(223,252)(224,256)(225,262)(226,258)(227,266)
(228,270)(229,261)(230,257)(231,265)(232,269)(233,263)(234,259)(235,267)
(236,271)(237,264)(238,260)(239,268)(240,272);
s3 := Sym(288)!( 1,113)( 2,125)( 3,121)( 4,117)( 5,116)( 6,128)( 7,124)
( 8,120)( 9,115)( 10,127)( 11,123)( 12,119)( 13,114)( 14,126)( 15,122)
( 16,118)( 17,129)( 18,141)( 19,137)( 20,133)( 21,132)( 22,144)( 23,140)
( 24,136)( 25,131)( 26,143)( 27,139)( 28,135)( 29,130)( 30,142)( 31,138)
( 32,134)( 33, 97)( 34,109)( 35,105)( 36,101)( 37,100)( 38,112)( 39,108)
( 40,104)( 41, 99)( 42,111)( 43,107)( 44,103)( 45, 98)( 46,110)( 47,106)
( 48,102)( 50, 61)( 51, 57)( 52, 53)( 54, 64)( 55, 60)( 58, 63)( 66, 77)
( 67, 73)( 68, 69)( 70, 80)( 71, 76)( 74, 79)( 82, 93)( 83, 89)( 84, 85)
( 86, 96)( 87, 92)( 90, 95)(145,257)(146,269)(147,265)(148,261)(149,260)
(150,272)(151,268)(152,264)(153,259)(154,271)(155,267)(156,263)(157,258)
(158,270)(159,266)(160,262)(161,273)(162,285)(163,281)(164,277)(165,276)
(166,288)(167,284)(168,280)(169,275)(170,287)(171,283)(172,279)(173,274)
(174,286)(175,282)(176,278)(177,241)(178,253)(179,249)(180,245)(181,244)
(182,256)(183,252)(184,248)(185,243)(186,255)(187,251)(188,247)(189,242)
(190,254)(191,250)(192,246)(194,205)(195,201)(196,197)(198,208)(199,204)
(202,207)(210,221)(211,217)(212,213)(214,224)(215,220)(218,223)(226,237)
(227,233)(228,229)(230,240)(231,236)(234,239);
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s3*s2*s1*s2*s0*s1*s2*s0*s3*s2*s1*s2*s0*s1*s3*s2*s3*s0*s1*s2*s0*s1 >;
References : None.
to this polytope