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