Polytope of Type {4,12,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,6}*1152k
if this polytope has a name.
Group : SmallGroup(1152,157851)
Rank : 4
Schlafli Type : {4,12,6}
Number of vertices, edges, etc : 4, 48, 72, 12
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
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 : {4,12,6}*576h
4-fold quotients : {4,6,6}*288d
12-fold quotients : {4,6,2}*96c
24-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)
( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)
( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)
( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)
( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)
(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)
(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)
(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)
(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)
(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)
(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)(200,208)
(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)(216,224)
(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)
(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)(248,256)
(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)(264,272)
(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)(280,288);;
s1 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 15)( 10, 16)( 11, 13)( 12, 14)
( 17, 35)( 18, 36)( 19, 33)( 20, 34)( 21, 39)( 22, 40)( 23, 37)( 24, 38)
( 25, 47)( 26, 48)( 27, 45)( 28, 46)( 29, 43)( 30, 44)( 31, 41)( 32, 42)
( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 63)( 58, 64)( 59, 61)( 60, 62)
( 65, 83)( 66, 84)( 67, 81)( 68, 82)( 69, 87)( 70, 88)( 71, 85)( 72, 86)
( 73, 95)( 74, 96)( 75, 93)( 76, 94)( 77, 91)( 78, 92)( 79, 89)( 80, 90)
( 97, 99)( 98,100)(101,103)(102,104)(105,111)(106,112)(107,109)(108,110)
(113,131)(114,132)(115,129)(116,130)(117,135)(118,136)(119,133)(120,134)
(121,143)(122,144)(123,141)(124,142)(125,139)(126,140)(127,137)(128,138)
(145,147)(146,148)(149,151)(150,152)(153,159)(154,160)(155,157)(156,158)
(161,179)(162,180)(163,177)(164,178)(165,183)(166,184)(167,181)(168,182)
(169,191)(170,192)(171,189)(172,190)(173,187)(174,188)(175,185)(176,186)
(193,195)(194,196)(197,199)(198,200)(201,207)(202,208)(203,205)(204,206)
(209,227)(210,228)(211,225)(212,226)(213,231)(214,232)(215,229)(216,230)
(217,239)(218,240)(219,237)(220,238)(221,235)(222,236)(223,233)(224,234)
(241,243)(242,244)(245,247)(246,248)(249,255)(250,256)(251,253)(252,254)
(257,275)(258,276)(259,273)(260,274)(261,279)(262,280)(263,277)(264,278)
(265,287)(266,288)(267,285)(268,286)(269,283)(270,284)(271,281)(272,282);;
s2 := ( 1, 17)( 2, 18)( 3, 20)( 4, 19)( 5, 29)( 6, 30)( 7, 32)( 8, 31)
( 9, 25)( 10, 26)( 11, 28)( 12, 27)( 13, 21)( 14, 22)( 15, 24)( 16, 23)
( 35, 36)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 43, 44)( 49,113)( 50,114)
( 51,116)( 52,115)( 53,125)( 54,126)( 55,128)( 56,127)( 57,121)( 58,122)
( 59,124)( 60,123)( 61,117)( 62,118)( 63,120)( 64,119)( 65, 97)( 66, 98)
( 67,100)( 68, 99)( 69,109)( 70,110)( 71,112)( 72,111)( 73,105)( 74,106)
( 75,108)( 76,107)( 77,101)( 78,102)( 79,104)( 80,103)( 81,129)( 82,130)
( 83,132)( 84,131)( 85,141)( 86,142)( 87,144)( 88,143)( 89,137)( 90,138)
( 91,140)( 92,139)( 93,133)( 94,134)( 95,136)( 96,135)(145,161)(146,162)
(147,164)(148,163)(149,173)(150,174)(151,176)(152,175)(153,169)(154,170)
(155,172)(156,171)(157,165)(158,166)(159,168)(160,167)(179,180)(181,189)
(182,190)(183,192)(184,191)(187,188)(193,257)(194,258)(195,260)(196,259)
(197,269)(198,270)(199,272)(200,271)(201,265)(202,266)(203,268)(204,267)
(205,261)(206,262)(207,264)(208,263)(209,241)(210,242)(211,244)(212,243)
(213,253)(214,254)(215,256)(216,255)(217,249)(218,250)(219,252)(220,251)
(221,245)(222,246)(223,248)(224,247)(225,273)(226,274)(227,276)(228,275)
(229,285)(230,286)(231,288)(232,287)(233,281)(234,282)(235,284)(236,283)
(237,277)(238,278)(239,280)(240,279);;
s3 := ( 1,193)( 2,196)( 3,195)( 4,194)( 5,197)( 6,200)( 7,199)( 8,198)
( 9,201)( 10,204)( 11,203)( 12,202)( 13,205)( 14,208)( 15,207)( 16,206)
( 17,209)( 18,212)( 19,211)( 20,210)( 21,213)( 22,216)( 23,215)( 24,214)
( 25,217)( 26,220)( 27,219)( 28,218)( 29,221)( 30,224)( 31,223)( 32,222)
( 33,225)( 34,228)( 35,227)( 36,226)( 37,229)( 38,232)( 39,231)( 40,230)
( 41,233)( 42,236)( 43,235)( 44,234)( 45,237)( 46,240)( 47,239)( 48,238)
( 49,145)( 50,148)( 51,147)( 52,146)( 53,149)( 54,152)( 55,151)( 56,150)
( 57,153)( 58,156)( 59,155)( 60,154)( 61,157)( 62,160)( 63,159)( 64,158)
( 65,161)( 66,164)( 67,163)( 68,162)( 69,165)( 70,168)( 71,167)( 72,166)
( 73,169)( 74,172)( 75,171)( 76,170)( 77,173)( 78,176)( 79,175)( 80,174)
( 81,177)( 82,180)( 83,179)( 84,178)( 85,181)( 86,184)( 87,183)( 88,182)
( 89,185)( 90,188)( 91,187)( 92,186)( 93,189)( 94,192)( 95,191)( 96,190)
( 97,241)( 98,244)( 99,243)(100,242)(101,245)(102,248)(103,247)(104,246)
(105,249)(106,252)(107,251)(108,250)(109,253)(110,256)(111,255)(112,254)
(113,257)(114,260)(115,259)(116,258)(117,261)(118,264)(119,263)(120,262)
(121,265)(122,268)(123,267)(124,266)(125,269)(126,272)(127,271)(128,270)
(129,273)(130,276)(131,275)(132,274)(133,277)(134,280)(135,279)(136,278)
(137,281)(138,284)(139,283)(140,282)(141,285)(142,288)(143,287)(144,286);;
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*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(288)!( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)
( 8, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)
( 24, 32)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)
( 40, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)
( 56, 64)( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)
( 72, 80)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)
(104,112)(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)
(120,128)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)
(136,144)(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)
(152,160)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)
(168,176)(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)
(184,192)(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)
(200,208)(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)
(216,224)(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)
(232,240)(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)
(248,256)(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)
(264,272)(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)
(280,288);
s1 := Sym(288)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 15)( 10, 16)( 11, 13)
( 12, 14)( 17, 35)( 18, 36)( 19, 33)( 20, 34)( 21, 39)( 22, 40)( 23, 37)
( 24, 38)( 25, 47)( 26, 48)( 27, 45)( 28, 46)( 29, 43)( 30, 44)( 31, 41)
( 32, 42)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 63)( 58, 64)( 59, 61)
( 60, 62)( 65, 83)( 66, 84)( 67, 81)( 68, 82)( 69, 87)( 70, 88)( 71, 85)
( 72, 86)( 73, 95)( 74, 96)( 75, 93)( 76, 94)( 77, 91)( 78, 92)( 79, 89)
( 80, 90)( 97, 99)( 98,100)(101,103)(102,104)(105,111)(106,112)(107,109)
(108,110)(113,131)(114,132)(115,129)(116,130)(117,135)(118,136)(119,133)
(120,134)(121,143)(122,144)(123,141)(124,142)(125,139)(126,140)(127,137)
(128,138)(145,147)(146,148)(149,151)(150,152)(153,159)(154,160)(155,157)
(156,158)(161,179)(162,180)(163,177)(164,178)(165,183)(166,184)(167,181)
(168,182)(169,191)(170,192)(171,189)(172,190)(173,187)(174,188)(175,185)
(176,186)(193,195)(194,196)(197,199)(198,200)(201,207)(202,208)(203,205)
(204,206)(209,227)(210,228)(211,225)(212,226)(213,231)(214,232)(215,229)
(216,230)(217,239)(218,240)(219,237)(220,238)(221,235)(222,236)(223,233)
(224,234)(241,243)(242,244)(245,247)(246,248)(249,255)(250,256)(251,253)
(252,254)(257,275)(258,276)(259,273)(260,274)(261,279)(262,280)(263,277)
(264,278)(265,287)(266,288)(267,285)(268,286)(269,283)(270,284)(271,281)
(272,282);
s2 := Sym(288)!( 1, 17)( 2, 18)( 3, 20)( 4, 19)( 5, 29)( 6, 30)( 7, 32)
( 8, 31)( 9, 25)( 10, 26)( 11, 28)( 12, 27)( 13, 21)( 14, 22)( 15, 24)
( 16, 23)( 35, 36)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 43, 44)( 49,113)
( 50,114)( 51,116)( 52,115)( 53,125)( 54,126)( 55,128)( 56,127)( 57,121)
( 58,122)( 59,124)( 60,123)( 61,117)( 62,118)( 63,120)( 64,119)( 65, 97)
( 66, 98)( 67,100)( 68, 99)( 69,109)( 70,110)( 71,112)( 72,111)( 73,105)
( 74,106)( 75,108)( 76,107)( 77,101)( 78,102)( 79,104)( 80,103)( 81,129)
( 82,130)( 83,132)( 84,131)( 85,141)( 86,142)( 87,144)( 88,143)( 89,137)
( 90,138)( 91,140)( 92,139)( 93,133)( 94,134)( 95,136)( 96,135)(145,161)
(146,162)(147,164)(148,163)(149,173)(150,174)(151,176)(152,175)(153,169)
(154,170)(155,172)(156,171)(157,165)(158,166)(159,168)(160,167)(179,180)
(181,189)(182,190)(183,192)(184,191)(187,188)(193,257)(194,258)(195,260)
(196,259)(197,269)(198,270)(199,272)(200,271)(201,265)(202,266)(203,268)
(204,267)(205,261)(206,262)(207,264)(208,263)(209,241)(210,242)(211,244)
(212,243)(213,253)(214,254)(215,256)(216,255)(217,249)(218,250)(219,252)
(220,251)(221,245)(222,246)(223,248)(224,247)(225,273)(226,274)(227,276)
(228,275)(229,285)(230,286)(231,288)(232,287)(233,281)(234,282)(235,284)
(236,283)(237,277)(238,278)(239,280)(240,279);
s3 := Sym(288)!( 1,193)( 2,196)( 3,195)( 4,194)( 5,197)( 6,200)( 7,199)
( 8,198)( 9,201)( 10,204)( 11,203)( 12,202)( 13,205)( 14,208)( 15,207)
( 16,206)( 17,209)( 18,212)( 19,211)( 20,210)( 21,213)( 22,216)( 23,215)
( 24,214)( 25,217)( 26,220)( 27,219)( 28,218)( 29,221)( 30,224)( 31,223)
( 32,222)( 33,225)( 34,228)( 35,227)( 36,226)( 37,229)( 38,232)( 39,231)
( 40,230)( 41,233)( 42,236)( 43,235)( 44,234)( 45,237)( 46,240)( 47,239)
( 48,238)( 49,145)( 50,148)( 51,147)( 52,146)( 53,149)( 54,152)( 55,151)
( 56,150)( 57,153)( 58,156)( 59,155)( 60,154)( 61,157)( 62,160)( 63,159)
( 64,158)( 65,161)( 66,164)( 67,163)( 68,162)( 69,165)( 70,168)( 71,167)
( 72,166)( 73,169)( 74,172)( 75,171)( 76,170)( 77,173)( 78,176)( 79,175)
( 80,174)( 81,177)( 82,180)( 83,179)( 84,178)( 85,181)( 86,184)( 87,183)
( 88,182)( 89,185)( 90,188)( 91,187)( 92,186)( 93,189)( 94,192)( 95,191)
( 96,190)( 97,241)( 98,244)( 99,243)(100,242)(101,245)(102,248)(103,247)
(104,246)(105,249)(106,252)(107,251)(108,250)(109,253)(110,256)(111,255)
(112,254)(113,257)(114,260)(115,259)(116,258)(117,261)(118,264)(119,263)
(120,262)(121,265)(122,268)(123,267)(124,266)(125,269)(126,272)(127,271)
(128,270)(129,273)(130,276)(131,275)(132,274)(133,277)(134,280)(135,279)
(136,278)(137,281)(138,284)(139,283)(140,282)(141,285)(142,288)(143,287)
(144,286);
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*s0*s1, s0*s1*s2*s1*s0*s1*s2*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2 >;
References : None.
to this polytope