Polytope of Type {3,4,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,4,6}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157852)
Rank : 4
Schlafli Type : {3,4,6}
Number of vertices, edges, etc : 12, 48, 96, 24
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 : {3,2,6}*72
32-fold quotients : {3,2,3}*36
48-fold quotients : {3,2,2}*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, 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, 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 := ( 1,257)( 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]);;
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,
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*s0*s2*s1*s0*s2*s1*s3*s2*s1*s3*s2*s0*s1*s2*s3*s2*s1*s2*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, 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, 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)!( 1,257)( 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>;
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, 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*s0*s2*s1*s0*s2*s1*s3*s2*s1*s3*s2*s0*s1*s2*s3*s2*s1*s2*s0*s1*s2*s0*s1 >;
References : None.
to this polytope