Polytope of Type {6,4,4,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,4,3}*1152c
if this polytope has a name.
Group : SmallGroup(1152,157852)
Rank : 5
Schlafli Type : {6,4,4,3}
Number of vertices, edges, etc : 6, 24, 16, 12, 3
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 4
Special Properties :
Universal
Non-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 : {3,4,4,3}*576
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, 11)( 2, 12)( 3, 9)( 4, 10)( 5, 15)( 6, 16)( 7, 13)( 8, 14)
( 17, 27)( 18, 28)( 19, 25)( 20, 26)( 21, 31)( 22, 32)( 23, 29)( 24, 30)
( 33, 43)( 34, 44)( 35, 41)( 36, 42)( 37, 47)( 38, 48)( 39, 45)( 40, 46)
( 49, 59)( 50, 60)( 51, 57)( 52, 58)( 53, 63)( 54, 64)( 55, 61)( 56, 62)
( 65, 75)( 66, 76)( 67, 73)( 68, 74)( 69, 79)( 70, 80)( 71, 77)( 72, 78)
( 81, 91)( 82, 92)( 83, 89)( 84, 90)( 85, 95)( 86, 96)( 87, 93)( 88, 94)
( 97,107)( 98,108)( 99,105)(100,106)(101,111)(102,112)(103,109)(104,110)
(113,123)(114,124)(115,121)(116,122)(117,127)(118,128)(119,125)(120,126)
(129,139)(130,140)(131,137)(132,138)(133,143)(134,144)(135,141)(136,142)
(145,155)(146,156)(147,153)(148,154)(149,159)(150,160)(151,157)(152,158)
(161,171)(162,172)(163,169)(164,170)(165,175)(166,176)(167,173)(168,174)
(177,187)(178,188)(179,185)(180,186)(181,191)(182,192)(183,189)(184,190)
(193,203)(194,204)(195,201)(196,202)(197,207)(198,208)(199,205)(200,206)
(209,219)(210,220)(211,217)(212,218)(213,223)(214,224)(215,221)(216,222)
(225,235)(226,236)(227,233)(228,234)(229,239)(230,240)(231,237)(232,238)
(241,251)(242,252)(243,249)(244,250)(245,255)(246,256)(247,253)(248,254)
(257,267)(258,268)(259,265)(260,266)(261,271)(262,272)(263,269)(264,270)
(273,283)(274,284)(275,281)(276,282)(277,287)(278,288)(279,285)(280,286);;
s3 := ( 2, 5)( 3, 13)( 4, 9)( 7, 14)( 8, 10)( 11, 16)( 18, 21)( 19, 29)
( 20, 25)( 23, 30)( 24, 26)( 27, 32)( 34, 37)( 35, 45)( 36, 41)( 39, 46)
( 40, 42)( 43, 48)( 49,129)( 50,133)( 51,141)( 52,137)( 53,130)( 54,134)
( 55,142)( 56,138)( 57,132)( 58,136)( 59,144)( 60,140)( 61,131)( 62,135)
( 63,143)( 64,139)( 65, 97)( 66,101)( 67,109)( 68,105)( 69, 98)( 70,102)
( 71,110)( 72,106)( 73,100)( 74,104)( 75,112)( 76,108)( 77, 99)( 78,103)
( 79,111)( 80,107)( 81,113)( 82,117)( 83,125)( 84,121)( 85,114)( 86,118)
( 87,126)( 88,122)( 89,116)( 90,120)( 91,128)( 92,124)( 93,115)( 94,119)
( 95,127)( 96,123)(146,149)(147,157)(148,153)(151,158)(152,154)(155,160)
(162,165)(163,173)(164,169)(167,174)(168,170)(171,176)(178,181)(179,189)
(180,185)(183,190)(184,186)(187,192)(193,273)(194,277)(195,285)(196,281)
(197,274)(198,278)(199,286)(200,282)(201,276)(202,280)(203,288)(204,284)
(205,275)(206,279)(207,287)(208,283)(209,241)(210,245)(211,253)(212,249)
(213,242)(214,246)(215,254)(216,250)(217,244)(218,248)(219,256)(220,252)
(221,243)(222,247)(223,255)(224,251)(225,257)(226,261)(227,269)(228,265)
(229,258)(230,262)(231,270)(232,266)(233,260)(234,264)(235,272)(236,268)
(237,259)(238,263)(239,271)(240,267);;
s4 := ( 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,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s1*s0*s2*s1*s2*s1*s0*s1, s4*s2*s3*s4*s2*s3*s4*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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, 11)( 2, 12)( 3, 9)( 4, 10)( 5, 15)( 6, 16)( 7, 13)
( 8, 14)( 17, 27)( 18, 28)( 19, 25)( 20, 26)( 21, 31)( 22, 32)( 23, 29)
( 24, 30)( 33, 43)( 34, 44)( 35, 41)( 36, 42)( 37, 47)( 38, 48)( 39, 45)
( 40, 46)( 49, 59)( 50, 60)( 51, 57)( 52, 58)( 53, 63)( 54, 64)( 55, 61)
( 56, 62)( 65, 75)( 66, 76)( 67, 73)( 68, 74)( 69, 79)( 70, 80)( 71, 77)
( 72, 78)( 81, 91)( 82, 92)( 83, 89)( 84, 90)( 85, 95)( 86, 96)( 87, 93)
( 88, 94)( 97,107)( 98,108)( 99,105)(100,106)(101,111)(102,112)(103,109)
(104,110)(113,123)(114,124)(115,121)(116,122)(117,127)(118,128)(119,125)
(120,126)(129,139)(130,140)(131,137)(132,138)(133,143)(134,144)(135,141)
(136,142)(145,155)(146,156)(147,153)(148,154)(149,159)(150,160)(151,157)
(152,158)(161,171)(162,172)(163,169)(164,170)(165,175)(166,176)(167,173)
(168,174)(177,187)(178,188)(179,185)(180,186)(181,191)(182,192)(183,189)
(184,190)(193,203)(194,204)(195,201)(196,202)(197,207)(198,208)(199,205)
(200,206)(209,219)(210,220)(211,217)(212,218)(213,223)(214,224)(215,221)
(216,222)(225,235)(226,236)(227,233)(228,234)(229,239)(230,240)(231,237)
(232,238)(241,251)(242,252)(243,249)(244,250)(245,255)(246,256)(247,253)
(248,254)(257,267)(258,268)(259,265)(260,266)(261,271)(262,272)(263,269)
(264,270)(273,283)(274,284)(275,281)(276,282)(277,287)(278,288)(279,285)
(280,286);
s3 := Sym(288)!( 2, 5)( 3, 13)( 4, 9)( 7, 14)( 8, 10)( 11, 16)( 18, 21)
( 19, 29)( 20, 25)( 23, 30)( 24, 26)( 27, 32)( 34, 37)( 35, 45)( 36, 41)
( 39, 46)( 40, 42)( 43, 48)( 49,129)( 50,133)( 51,141)( 52,137)( 53,130)
( 54,134)( 55,142)( 56,138)( 57,132)( 58,136)( 59,144)( 60,140)( 61,131)
( 62,135)( 63,143)( 64,139)( 65, 97)( 66,101)( 67,109)( 68,105)( 69, 98)
( 70,102)( 71,110)( 72,106)( 73,100)( 74,104)( 75,112)( 76,108)( 77, 99)
( 78,103)( 79,111)( 80,107)( 81,113)( 82,117)( 83,125)( 84,121)( 85,114)
( 86,118)( 87,126)( 88,122)( 89,116)( 90,120)( 91,128)( 92,124)( 93,115)
( 94,119)( 95,127)( 96,123)(146,149)(147,157)(148,153)(151,158)(152,154)
(155,160)(162,165)(163,173)(164,169)(167,174)(168,170)(171,176)(178,181)
(179,189)(180,185)(183,190)(184,186)(187,192)(193,273)(194,277)(195,285)
(196,281)(197,274)(198,278)(199,286)(200,282)(201,276)(202,280)(203,288)
(204,284)(205,275)(206,279)(207,287)(208,283)(209,241)(210,245)(211,253)
(212,249)(213,242)(214,246)(215,254)(216,250)(217,244)(218,248)(219,256)
(220,252)(221,243)(222,247)(223,255)(224,251)(225,257)(226,261)(227,269)
(228,265)(229,258)(230,262)(231,270)(232,266)(233,260)(234,264)(235,272)
(236,268)(237,259)(238,263)(239,271)(240,267);
s4 := 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,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s1*s0*s2*s1*s2*s1*s0*s1,
s4*s2*s3*s4*s2*s3*s4*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope