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