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