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