Polytope of Type {6,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,4}*1152f
if this polytope has a name.
Group : SmallGroup(1152,157640)
Rank : 4
Schlafli Type : {6,6,4}
Number of vertices, edges, etc : 24, 72, 48, 4
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 : {3,6,4}*576a, {6,6,2}*576b
3-fold quotients : {6,6,4}*384
4-fold quotients : {6,6,4}*288c, {3,6,2}*288
6-fold quotients : {3,6,4}*192, {6,6,2}*192
8-fold quotients : {3,6,4}*144, {6,6,2}*144c
12-fold quotients : {6,2,4}*96, {3,6,2}*96, {6,3,2}*96
16-fold quotients : {3,6,2}*72
24-fold quotients : {3,2,4}*48, {3,3,2}*48, {6,2,2}*48
36-fold quotients : {2,2,4}*32
48-fold quotients : {3,2,2}*24
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 25)( 14, 26)( 15, 28)
( 16, 27)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 29)( 22, 30)( 23, 32)
( 24, 31)( 39, 40)( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 49, 61)( 50, 62)
( 51, 64)( 52, 63)( 53, 69)( 54, 70)( 55, 72)( 56, 71)( 57, 65)( 58, 66)
( 59, 68)( 60, 67)( 75, 76)( 77, 81)( 78, 82)( 79, 84)( 80, 83)( 85, 97)
( 86, 98)( 87,100)( 88, 99)( 89,105)( 90,106)( 91,108)( 92,107)( 93,101)
( 94,102)( 95,104)( 96,103)(111,112)(113,117)(114,118)(115,120)(116,119)
(121,133)(122,134)(123,136)(124,135)(125,141)(126,142)(127,144)(128,143)
(129,137)(130,138)(131,140)(132,139)(147,148)(149,153)(150,154)(151,156)
(152,155)(157,169)(158,170)(159,172)(160,171)(161,177)(162,178)(163,180)
(164,179)(165,173)(166,174)(167,176)(168,175)(183,184)(185,189)(186,190)
(187,192)(188,191)(193,205)(194,206)(195,208)(196,207)(197,213)(198,214)
(199,216)(200,215)(201,209)(202,210)(203,212)(204,211)(219,220)(221,225)
(222,226)(223,228)(224,227)(229,241)(230,242)(231,244)(232,243)(233,249)
(234,250)(235,252)(236,251)(237,245)(238,246)(239,248)(240,247)(255,256)
(257,261)(258,262)(259,264)(260,263)(265,277)(266,278)(267,280)(268,279)
(269,285)(270,286)(271,288)(272,287)(273,281)(274,282)(275,284)(276,283);;
s1 := ( 1,161)( 2,164)( 3,163)( 4,162)( 5,157)( 6,160)( 7,159)( 8,158)
( 9,165)( 10,168)( 11,167)( 12,166)( 13,149)( 14,152)( 15,151)( 16,150)
( 17,145)( 18,148)( 19,147)( 20,146)( 21,153)( 22,156)( 23,155)( 24,154)
( 25,173)( 26,176)( 27,175)( 28,174)( 29,169)( 30,172)( 31,171)( 32,170)
( 33,177)( 34,180)( 35,179)( 36,178)( 37,197)( 38,200)( 39,199)( 40,198)
( 41,193)( 42,196)( 43,195)( 44,194)( 45,201)( 46,204)( 47,203)( 48,202)
( 49,185)( 50,188)( 51,187)( 52,186)( 53,181)( 54,184)( 55,183)( 56,182)
( 57,189)( 58,192)( 59,191)( 60,190)( 61,209)( 62,212)( 63,211)( 64,210)
( 65,205)( 66,208)( 67,207)( 68,206)( 69,213)( 70,216)( 71,215)( 72,214)
( 73,233)( 74,236)( 75,235)( 76,234)( 77,229)( 78,232)( 79,231)( 80,230)
( 81,237)( 82,240)( 83,239)( 84,238)( 85,221)( 86,224)( 87,223)( 88,222)
( 89,217)( 90,220)( 91,219)( 92,218)( 93,225)( 94,228)( 95,227)( 96,226)
( 97,245)( 98,248)( 99,247)(100,246)(101,241)(102,244)(103,243)(104,242)
(105,249)(106,252)(107,251)(108,250)(109,269)(110,272)(111,271)(112,270)
(113,265)(114,268)(115,267)(116,266)(117,273)(118,276)(119,275)(120,274)
(121,257)(122,260)(123,259)(124,258)(125,253)(126,256)(127,255)(128,254)
(129,261)(130,264)(131,263)(132,262)(133,281)(134,284)(135,283)(136,282)
(137,277)(138,280)(139,279)(140,278)(141,285)(142,288)(143,287)(144,286);;
s2 := ( 1, 2)( 5, 6)( 9, 10)( 13, 26)( 14, 25)( 15, 27)( 16, 28)( 17, 30)
( 18, 29)( 19, 31)( 20, 32)( 21, 34)( 22, 33)( 23, 35)( 24, 36)( 37, 38)
( 41, 42)( 45, 46)( 49, 62)( 50, 61)( 51, 63)( 52, 64)( 53, 66)( 54, 65)
( 55, 67)( 56, 68)( 57, 70)( 58, 69)( 59, 71)( 60, 72)( 73,110)( 74,109)
( 75,111)( 76,112)( 77,114)( 78,113)( 79,115)( 80,116)( 81,118)( 82,117)
( 83,119)( 84,120)( 85,134)( 86,133)( 87,135)( 88,136)( 89,138)( 90,137)
( 91,139)( 92,140)( 93,142)( 94,141)( 95,143)( 96,144)( 97,122)( 98,121)
( 99,123)(100,124)(101,126)(102,125)(103,127)(104,128)(105,130)(106,129)
(107,131)(108,132)(145,146)(149,150)(153,154)(157,170)(158,169)(159,171)
(160,172)(161,174)(162,173)(163,175)(164,176)(165,178)(166,177)(167,179)
(168,180)(181,182)(185,186)(189,190)(193,206)(194,205)(195,207)(196,208)
(197,210)(198,209)(199,211)(200,212)(201,214)(202,213)(203,215)(204,216)
(217,254)(218,253)(219,255)(220,256)(221,258)(222,257)(223,259)(224,260)
(225,262)(226,261)(227,263)(228,264)(229,278)(230,277)(231,279)(232,280)
(233,282)(234,281)(235,283)(236,284)(237,286)(238,285)(239,287)(240,288)
(241,266)(242,265)(243,267)(244,268)(245,270)(246,269)(247,271)(248,272)
(249,274)(250,273)(251,275)(252,276);;
s3 := ( 1, 73)( 2, 74)( 3, 75)( 4, 76)( 5, 77)( 6, 78)( 7, 79)( 8, 80)
( 9, 81)( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)
( 17, 89)( 18, 90)( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)( 24, 96)
( 25, 97)( 26, 98)( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)( 32,104)
( 33,105)( 34,106)( 35,107)( 36,108)( 37,109)( 38,110)( 39,111)( 40,112)
( 41,113)( 42,114)( 43,115)( 44,116)( 45,117)( 46,118)( 47,119)( 48,120)
( 49,121)( 50,122)( 51,123)( 52,124)( 53,125)( 54,126)( 55,127)( 56,128)
( 57,129)( 58,130)( 59,131)( 60,132)( 61,133)( 62,134)( 63,135)( 64,136)
( 65,137)( 66,138)( 67,139)( 68,140)( 69,141)( 70,142)( 71,143)( 72,144)
(145,217)(146,218)(147,219)(148,220)(149,221)(150,222)(151,223)(152,224)
(153,225)(154,226)(155,227)(156,228)(157,229)(158,230)(159,231)(160,232)
(161,233)(162,234)(163,235)(164,236)(165,237)(166,238)(167,239)(168,240)
(169,241)(170,242)(171,243)(172,244)(173,245)(174,246)(175,247)(176,248)
(177,249)(178,250)(179,251)(180,252)(181,253)(182,254)(183,255)(184,256)
(185,257)(186,258)(187,259)(188,260)(189,261)(190,262)(191,263)(192,264)
(193,265)(194,266)(195,267)(196,268)(197,269)(198,270)(199,271)(200,272)
(201,273)(202,274)(203,275)(204,276)(205,277)(206,278)(207,279)(208,280)
(209,281)(210,282)(211,283)(212,284)(213,285)(214,286)(215,287)(216,288);;
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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(288)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 25)( 14, 26)
( 15, 28)( 16, 27)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 29)( 22, 30)
( 23, 32)( 24, 31)( 39, 40)( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 49, 61)
( 50, 62)( 51, 64)( 52, 63)( 53, 69)( 54, 70)( 55, 72)( 56, 71)( 57, 65)
( 58, 66)( 59, 68)( 60, 67)( 75, 76)( 77, 81)( 78, 82)( 79, 84)( 80, 83)
( 85, 97)( 86, 98)( 87,100)( 88, 99)( 89,105)( 90,106)( 91,108)( 92,107)
( 93,101)( 94,102)( 95,104)( 96,103)(111,112)(113,117)(114,118)(115,120)
(116,119)(121,133)(122,134)(123,136)(124,135)(125,141)(126,142)(127,144)
(128,143)(129,137)(130,138)(131,140)(132,139)(147,148)(149,153)(150,154)
(151,156)(152,155)(157,169)(158,170)(159,172)(160,171)(161,177)(162,178)
(163,180)(164,179)(165,173)(166,174)(167,176)(168,175)(183,184)(185,189)
(186,190)(187,192)(188,191)(193,205)(194,206)(195,208)(196,207)(197,213)
(198,214)(199,216)(200,215)(201,209)(202,210)(203,212)(204,211)(219,220)
(221,225)(222,226)(223,228)(224,227)(229,241)(230,242)(231,244)(232,243)
(233,249)(234,250)(235,252)(236,251)(237,245)(238,246)(239,248)(240,247)
(255,256)(257,261)(258,262)(259,264)(260,263)(265,277)(266,278)(267,280)
(268,279)(269,285)(270,286)(271,288)(272,287)(273,281)(274,282)(275,284)
(276,283);
s1 := Sym(288)!( 1,161)( 2,164)( 3,163)( 4,162)( 5,157)( 6,160)( 7,159)
( 8,158)( 9,165)( 10,168)( 11,167)( 12,166)( 13,149)( 14,152)( 15,151)
( 16,150)( 17,145)( 18,148)( 19,147)( 20,146)( 21,153)( 22,156)( 23,155)
( 24,154)( 25,173)( 26,176)( 27,175)( 28,174)( 29,169)( 30,172)( 31,171)
( 32,170)( 33,177)( 34,180)( 35,179)( 36,178)( 37,197)( 38,200)( 39,199)
( 40,198)( 41,193)( 42,196)( 43,195)( 44,194)( 45,201)( 46,204)( 47,203)
( 48,202)( 49,185)( 50,188)( 51,187)( 52,186)( 53,181)( 54,184)( 55,183)
( 56,182)( 57,189)( 58,192)( 59,191)( 60,190)( 61,209)( 62,212)( 63,211)
( 64,210)( 65,205)( 66,208)( 67,207)( 68,206)( 69,213)( 70,216)( 71,215)
( 72,214)( 73,233)( 74,236)( 75,235)( 76,234)( 77,229)( 78,232)( 79,231)
( 80,230)( 81,237)( 82,240)( 83,239)( 84,238)( 85,221)( 86,224)( 87,223)
( 88,222)( 89,217)( 90,220)( 91,219)( 92,218)( 93,225)( 94,228)( 95,227)
( 96,226)( 97,245)( 98,248)( 99,247)(100,246)(101,241)(102,244)(103,243)
(104,242)(105,249)(106,252)(107,251)(108,250)(109,269)(110,272)(111,271)
(112,270)(113,265)(114,268)(115,267)(116,266)(117,273)(118,276)(119,275)
(120,274)(121,257)(122,260)(123,259)(124,258)(125,253)(126,256)(127,255)
(128,254)(129,261)(130,264)(131,263)(132,262)(133,281)(134,284)(135,283)
(136,282)(137,277)(138,280)(139,279)(140,278)(141,285)(142,288)(143,287)
(144,286);
s2 := Sym(288)!( 1, 2)( 5, 6)( 9, 10)( 13, 26)( 14, 25)( 15, 27)( 16, 28)
( 17, 30)( 18, 29)( 19, 31)( 20, 32)( 21, 34)( 22, 33)( 23, 35)( 24, 36)
( 37, 38)( 41, 42)( 45, 46)( 49, 62)( 50, 61)( 51, 63)( 52, 64)( 53, 66)
( 54, 65)( 55, 67)( 56, 68)( 57, 70)( 58, 69)( 59, 71)( 60, 72)( 73,110)
( 74,109)( 75,111)( 76,112)( 77,114)( 78,113)( 79,115)( 80,116)( 81,118)
( 82,117)( 83,119)( 84,120)( 85,134)( 86,133)( 87,135)( 88,136)( 89,138)
( 90,137)( 91,139)( 92,140)( 93,142)( 94,141)( 95,143)( 96,144)( 97,122)
( 98,121)( 99,123)(100,124)(101,126)(102,125)(103,127)(104,128)(105,130)
(106,129)(107,131)(108,132)(145,146)(149,150)(153,154)(157,170)(158,169)
(159,171)(160,172)(161,174)(162,173)(163,175)(164,176)(165,178)(166,177)
(167,179)(168,180)(181,182)(185,186)(189,190)(193,206)(194,205)(195,207)
(196,208)(197,210)(198,209)(199,211)(200,212)(201,214)(202,213)(203,215)
(204,216)(217,254)(218,253)(219,255)(220,256)(221,258)(222,257)(223,259)
(224,260)(225,262)(226,261)(227,263)(228,264)(229,278)(230,277)(231,279)
(232,280)(233,282)(234,281)(235,283)(236,284)(237,286)(238,285)(239,287)
(240,288)(241,266)(242,265)(243,267)(244,268)(245,270)(246,269)(247,271)
(248,272)(249,274)(250,273)(251,275)(252,276);
s3 := Sym(288)!( 1, 73)( 2, 74)( 3, 75)( 4, 76)( 5, 77)( 6, 78)( 7, 79)
( 8, 80)( 9, 81)( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)
( 16, 88)( 17, 89)( 18, 90)( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)
( 24, 96)( 25, 97)( 26, 98)( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)
( 32,104)( 33,105)( 34,106)( 35,107)( 36,108)( 37,109)( 38,110)( 39,111)
( 40,112)( 41,113)( 42,114)( 43,115)( 44,116)( 45,117)( 46,118)( 47,119)
( 48,120)( 49,121)( 50,122)( 51,123)( 52,124)( 53,125)( 54,126)( 55,127)
( 56,128)( 57,129)( 58,130)( 59,131)( 60,132)( 61,133)( 62,134)( 63,135)
( 64,136)( 65,137)( 66,138)( 67,139)( 68,140)( 69,141)( 70,142)( 71,143)
( 72,144)(145,217)(146,218)(147,219)(148,220)(149,221)(150,222)(151,223)
(152,224)(153,225)(154,226)(155,227)(156,228)(157,229)(158,230)(159,231)
(160,232)(161,233)(162,234)(163,235)(164,236)(165,237)(166,238)(167,239)
(168,240)(169,241)(170,242)(171,243)(172,244)(173,245)(174,246)(175,247)
(176,248)(177,249)(178,250)(179,251)(180,252)(181,253)(182,254)(183,255)
(184,256)(185,257)(186,258)(187,259)(188,260)(189,261)(190,262)(191,263)
(192,264)(193,265)(194,266)(195,267)(196,268)(197,269)(198,270)(199,271)
(200,272)(201,273)(202,274)(203,275)(204,276)(205,277)(206,278)(207,279)
(208,280)(209,281)(210,282)(211,283)(212,284)(213,285)(214,286)(215,287)
(216,288);
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,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 >;
References : None.
to this polytope