Polytope of Type {6,12,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12,4}*1152e
if this polytope has a name.
Group : SmallGroup(1152,157549)
Rank : 4
Schlafli Type : {6,12,4}
Number of vertices, edges, etc : 6, 72, 48, 8
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
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 : {6,12,4}*576d, {6,12,4}*576e, {6,6,4}*576a
3-fold quotients : {2,12,4}*384b
4-fold quotients : {6,12,2}*288a, {6,6,4}*288d
6-fold quotients : {2,12,4}*192b, {2,12,4}*192c, {2,6,4}*192
8-fold quotients : {6,6,2}*144a
12-fold quotients : {2,12,2}*96, {6,4,2}*96a, {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
24-fold quotients : {2,3,4}*48, {2,6,2}*48, {6,2,2}*48
36-fold quotients : {2,4,2}*32
48-fold quotients : {2,3,2}*24, {3,2,2}*24
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 5, 9)( 6, 10)( 7, 11)( 8, 12)( 17, 21)( 18, 22)( 19, 23)( 20, 24)
( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 41, 45)( 42, 46)( 43, 47)( 44, 48)
( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 65, 69)( 66, 70)( 67, 71)( 68, 72)
( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 89, 93)( 90, 94)( 91, 95)( 92, 96)
(101,105)(102,106)(103,107)(104,108)(113,117)(114,118)(115,119)(116,120)
(125,129)(126,130)(127,131)(128,132)(137,141)(138,142)(139,143)(140,144)
(149,153)(150,154)(151,155)(152,156)(161,165)(162,166)(163,167)(164,168)
(173,177)(174,178)(175,179)(176,180)(185,189)(186,190)(187,191)(188,192)
(197,201)(198,202)(199,203)(200,204)(209,213)(210,214)(211,215)(212,216)
(221,225)(222,226)(223,227)(224,228)(233,237)(234,238)(235,239)(236,240)
(245,249)(246,250)(247,251)(248,252)(257,261)(258,262)(259,263)(260,264)
(269,273)(270,274)(271,275)(272,276)(281,285)(282,286)(283,287)(284,288);;
s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 11, 12)( 13, 29)( 14, 30)( 15, 32)
( 16, 31)( 17, 25)( 18, 26)( 19, 28)( 20, 27)( 21, 33)( 22, 34)( 23, 36)
( 24, 35)( 37, 41)( 38, 42)( 39, 44)( 40, 43)( 47, 48)( 49, 65)( 50, 66)
( 51, 68)( 52, 67)( 53, 61)( 54, 62)( 55, 64)( 56, 63)( 57, 69)( 58, 70)
( 59, 72)( 60, 71)( 73,113)( 74,114)( 75,116)( 76,115)( 77,109)( 78,110)
( 79,112)( 80,111)( 81,117)( 82,118)( 83,120)( 84,119)( 85,137)( 86,138)
( 87,140)( 88,139)( 89,133)( 90,134)( 91,136)( 92,135)( 93,141)( 94,142)
( 95,144)( 96,143)( 97,125)( 98,126)( 99,128)(100,127)(101,121)(102,122)
(103,124)(104,123)(105,129)(106,130)(107,132)(108,131)(145,149)(146,150)
(147,152)(148,151)(155,156)(157,173)(158,174)(159,176)(160,175)(161,169)
(162,170)(163,172)(164,171)(165,177)(166,178)(167,180)(168,179)(181,185)
(182,186)(183,188)(184,187)(191,192)(193,209)(194,210)(195,212)(196,211)
(197,205)(198,206)(199,208)(200,207)(201,213)(202,214)(203,216)(204,215)
(217,257)(218,258)(219,260)(220,259)(221,253)(222,254)(223,256)(224,255)
(225,261)(226,262)(227,264)(228,263)(229,281)(230,282)(231,284)(232,283)
(233,277)(234,278)(235,280)(236,279)(237,285)(238,286)(239,288)(240,287)
(241,269)(242,270)(243,272)(244,271)(245,265)(246,266)(247,268)(248,267)
(249,273)(250,274)(251,276)(252,275);;
s2 := ( 1, 85)( 2, 88)( 3, 87)( 4, 86)( 5, 89)( 6, 92)( 7, 91)( 8, 90)
( 9, 93)( 10, 96)( 11, 95)( 12, 94)( 13, 73)( 14, 76)( 15, 75)( 16, 74)
( 17, 77)( 18, 80)( 19, 79)( 20, 78)( 21, 81)( 22, 84)( 23, 83)( 24, 82)
( 25, 97)( 26,100)( 27, 99)( 28, 98)( 29,101)( 30,104)( 31,103)( 32,102)
( 33,105)( 34,108)( 35,107)( 36,106)( 37,121)( 38,124)( 39,123)( 40,122)
( 41,125)( 42,128)( 43,127)( 44,126)( 45,129)( 46,132)( 47,131)( 48,130)
( 49,109)( 50,112)( 51,111)( 52,110)( 53,113)( 54,116)( 55,115)( 56,114)
( 57,117)( 58,120)( 59,119)( 60,118)( 61,133)( 62,136)( 63,135)( 64,134)
( 65,137)( 66,140)( 67,139)( 68,138)( 69,141)( 70,144)( 71,143)( 72,142)
(145,229)(146,232)(147,231)(148,230)(149,233)(150,236)(151,235)(152,234)
(153,237)(154,240)(155,239)(156,238)(157,217)(158,220)(159,219)(160,218)
(161,221)(162,224)(163,223)(164,222)(165,225)(166,228)(167,227)(168,226)
(169,241)(170,244)(171,243)(172,242)(173,245)(174,248)(175,247)(176,246)
(177,249)(178,252)(179,251)(180,250)(181,265)(182,268)(183,267)(184,266)
(185,269)(186,272)(187,271)(188,270)(189,273)(190,276)(191,275)(192,274)
(193,253)(194,256)(195,255)(196,254)(197,257)(198,260)(199,259)(200,258)
(201,261)(202,264)(203,263)(204,262)(205,277)(206,280)(207,279)(208,278)
(209,281)(210,284)(211,283)(212,282)(213,285)(214,288)(215,287)(216,286);;
s3 := ( 1,146)( 2,145)( 3,148)( 4,147)( 5,150)( 6,149)( 7,152)( 8,151)
( 9,154)( 10,153)( 11,156)( 12,155)( 13,158)( 14,157)( 15,160)( 16,159)
( 17,162)( 18,161)( 19,164)( 20,163)( 21,166)( 22,165)( 23,168)( 24,167)
( 25,170)( 26,169)( 27,172)( 28,171)( 29,174)( 30,173)( 31,176)( 32,175)
( 33,178)( 34,177)( 35,180)( 36,179)( 37,182)( 38,181)( 39,184)( 40,183)
( 41,186)( 42,185)( 43,188)( 44,187)( 45,190)( 46,189)( 47,192)( 48,191)
( 49,194)( 50,193)( 51,196)( 52,195)( 53,198)( 54,197)( 55,200)( 56,199)
( 57,202)( 58,201)( 59,204)( 60,203)( 61,206)( 62,205)( 63,208)( 64,207)
( 65,210)( 66,209)( 67,212)( 68,211)( 69,214)( 70,213)( 71,216)( 72,215)
( 73,218)( 74,217)( 75,220)( 76,219)( 77,222)( 78,221)( 79,224)( 80,223)
( 81,226)( 82,225)( 83,228)( 84,227)( 85,230)( 86,229)( 87,232)( 88,231)
( 89,234)( 90,233)( 91,236)( 92,235)( 93,238)( 94,237)( 95,240)( 96,239)
( 97,242)( 98,241)( 99,244)(100,243)(101,246)(102,245)(103,248)(104,247)
(105,250)(106,249)(107,252)(108,251)(109,254)(110,253)(111,256)(112,255)
(113,258)(114,257)(115,260)(116,259)(117,262)(118,261)(119,264)(120,263)
(121,266)(122,265)(123,268)(124,267)(125,270)(126,269)(127,272)(128,271)
(129,274)(130,273)(131,276)(132,275)(133,278)(134,277)(135,280)(136,279)
(137,282)(138,281)(139,284)(140,283)(141,286)(142,285)(143,288)(144,287);;
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*s2*s1*s0*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(288)!( 5, 9)( 6, 10)( 7, 11)( 8, 12)( 17, 21)( 18, 22)( 19, 23)
( 20, 24)( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 41, 45)( 42, 46)( 43, 47)
( 44, 48)( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 65, 69)( 66, 70)( 67, 71)
( 68, 72)( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 89, 93)( 90, 94)( 91, 95)
( 92, 96)(101,105)(102,106)(103,107)(104,108)(113,117)(114,118)(115,119)
(116,120)(125,129)(126,130)(127,131)(128,132)(137,141)(138,142)(139,143)
(140,144)(149,153)(150,154)(151,155)(152,156)(161,165)(162,166)(163,167)
(164,168)(173,177)(174,178)(175,179)(176,180)(185,189)(186,190)(187,191)
(188,192)(197,201)(198,202)(199,203)(200,204)(209,213)(210,214)(211,215)
(212,216)(221,225)(222,226)(223,227)(224,228)(233,237)(234,238)(235,239)
(236,240)(245,249)(246,250)(247,251)(248,252)(257,261)(258,262)(259,263)
(260,264)(269,273)(270,274)(271,275)(272,276)(281,285)(282,286)(283,287)
(284,288);
s1 := Sym(288)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 11, 12)( 13, 29)( 14, 30)
( 15, 32)( 16, 31)( 17, 25)( 18, 26)( 19, 28)( 20, 27)( 21, 33)( 22, 34)
( 23, 36)( 24, 35)( 37, 41)( 38, 42)( 39, 44)( 40, 43)( 47, 48)( 49, 65)
( 50, 66)( 51, 68)( 52, 67)( 53, 61)( 54, 62)( 55, 64)( 56, 63)( 57, 69)
( 58, 70)( 59, 72)( 60, 71)( 73,113)( 74,114)( 75,116)( 76,115)( 77,109)
( 78,110)( 79,112)( 80,111)( 81,117)( 82,118)( 83,120)( 84,119)( 85,137)
( 86,138)( 87,140)( 88,139)( 89,133)( 90,134)( 91,136)( 92,135)( 93,141)
( 94,142)( 95,144)( 96,143)( 97,125)( 98,126)( 99,128)(100,127)(101,121)
(102,122)(103,124)(104,123)(105,129)(106,130)(107,132)(108,131)(145,149)
(146,150)(147,152)(148,151)(155,156)(157,173)(158,174)(159,176)(160,175)
(161,169)(162,170)(163,172)(164,171)(165,177)(166,178)(167,180)(168,179)
(181,185)(182,186)(183,188)(184,187)(191,192)(193,209)(194,210)(195,212)
(196,211)(197,205)(198,206)(199,208)(200,207)(201,213)(202,214)(203,216)
(204,215)(217,257)(218,258)(219,260)(220,259)(221,253)(222,254)(223,256)
(224,255)(225,261)(226,262)(227,264)(228,263)(229,281)(230,282)(231,284)
(232,283)(233,277)(234,278)(235,280)(236,279)(237,285)(238,286)(239,288)
(240,287)(241,269)(242,270)(243,272)(244,271)(245,265)(246,266)(247,268)
(248,267)(249,273)(250,274)(251,276)(252,275);
s2 := Sym(288)!( 1, 85)( 2, 88)( 3, 87)( 4, 86)( 5, 89)( 6, 92)( 7, 91)
( 8, 90)( 9, 93)( 10, 96)( 11, 95)( 12, 94)( 13, 73)( 14, 76)( 15, 75)
( 16, 74)( 17, 77)( 18, 80)( 19, 79)( 20, 78)( 21, 81)( 22, 84)( 23, 83)
( 24, 82)( 25, 97)( 26,100)( 27, 99)( 28, 98)( 29,101)( 30,104)( 31,103)
( 32,102)( 33,105)( 34,108)( 35,107)( 36,106)( 37,121)( 38,124)( 39,123)
( 40,122)( 41,125)( 42,128)( 43,127)( 44,126)( 45,129)( 46,132)( 47,131)
( 48,130)( 49,109)( 50,112)( 51,111)( 52,110)( 53,113)( 54,116)( 55,115)
( 56,114)( 57,117)( 58,120)( 59,119)( 60,118)( 61,133)( 62,136)( 63,135)
( 64,134)( 65,137)( 66,140)( 67,139)( 68,138)( 69,141)( 70,144)( 71,143)
( 72,142)(145,229)(146,232)(147,231)(148,230)(149,233)(150,236)(151,235)
(152,234)(153,237)(154,240)(155,239)(156,238)(157,217)(158,220)(159,219)
(160,218)(161,221)(162,224)(163,223)(164,222)(165,225)(166,228)(167,227)
(168,226)(169,241)(170,244)(171,243)(172,242)(173,245)(174,248)(175,247)
(176,246)(177,249)(178,252)(179,251)(180,250)(181,265)(182,268)(183,267)
(184,266)(185,269)(186,272)(187,271)(188,270)(189,273)(190,276)(191,275)
(192,274)(193,253)(194,256)(195,255)(196,254)(197,257)(198,260)(199,259)
(200,258)(201,261)(202,264)(203,263)(204,262)(205,277)(206,280)(207,279)
(208,278)(209,281)(210,284)(211,283)(212,282)(213,285)(214,288)(215,287)
(216,286);
s3 := Sym(288)!( 1,146)( 2,145)( 3,148)( 4,147)( 5,150)( 6,149)( 7,152)
( 8,151)( 9,154)( 10,153)( 11,156)( 12,155)( 13,158)( 14,157)( 15,160)
( 16,159)( 17,162)( 18,161)( 19,164)( 20,163)( 21,166)( 22,165)( 23,168)
( 24,167)( 25,170)( 26,169)( 27,172)( 28,171)( 29,174)( 30,173)( 31,176)
( 32,175)( 33,178)( 34,177)( 35,180)( 36,179)( 37,182)( 38,181)( 39,184)
( 40,183)( 41,186)( 42,185)( 43,188)( 44,187)( 45,190)( 46,189)( 47,192)
( 48,191)( 49,194)( 50,193)( 51,196)( 52,195)( 53,198)( 54,197)( 55,200)
( 56,199)( 57,202)( 58,201)( 59,204)( 60,203)( 61,206)( 62,205)( 63,208)
( 64,207)( 65,210)( 66,209)( 67,212)( 68,211)( 69,214)( 70,213)( 71,216)
( 72,215)( 73,218)( 74,217)( 75,220)( 76,219)( 77,222)( 78,221)( 79,224)
( 80,223)( 81,226)( 82,225)( 83,228)( 84,227)( 85,230)( 86,229)( 87,232)
( 88,231)( 89,234)( 90,233)( 91,236)( 92,235)( 93,238)( 94,237)( 95,240)
( 96,239)( 97,242)( 98,241)( 99,244)(100,243)(101,246)(102,245)(103,248)
(104,247)(105,250)(106,249)(107,252)(108,251)(109,254)(110,253)(111,256)
(112,255)(113,258)(114,257)(115,260)(116,259)(117,262)(118,261)(119,264)
(120,263)(121,266)(122,265)(123,268)(124,267)(125,270)(126,269)(127,272)
(128,271)(129,274)(130,273)(131,276)(132,275)(133,278)(134,277)(135,280)
(136,279)(137,282)(138,281)(139,284)(140,283)(141,286)(142,285)(143,288)
(144,287);
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*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope