Polytope of Type {3,6,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,6,4}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157851)
Rank : 5
Schlafli Type : {3,6,6,4}
Number of vertices, edges, etc : 4, 12, 24, 12, 4
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 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) :
No Regular Quotients.
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, 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);;
s2 := ( 1, 2)( 5, 6)( 9, 14)( 10, 13)( 11, 15)( 12, 16)( 17, 34)( 18, 33)
( 19, 35)( 20, 36)( 21, 38)( 22, 37)( 23, 39)( 24, 40)( 25, 46)( 26, 45)
( 27, 47)( 28, 48)( 29, 42)( 30, 41)( 31, 43)( 32, 44)( 49, 98)( 50, 97)
( 51, 99)( 52,100)( 53,102)( 54,101)( 55,103)( 56,104)( 57,110)( 58,109)
( 59,111)( 60,112)( 61,106)( 62,105)( 63,107)( 64,108)( 65,130)( 66,129)
( 67,131)( 68,132)( 69,134)( 70,133)( 71,135)( 72,136)( 73,142)( 74,141)
( 75,143)( 76,144)( 77,138)( 78,137)( 79,139)( 80,140)( 81,114)( 82,113)
( 83,115)( 84,116)( 85,118)( 86,117)( 87,119)( 88,120)( 89,126)( 90,125)
( 91,127)( 92,128)( 93,122)( 94,121)( 95,123)( 96,124)(145,146)(149,150)
(153,158)(154,157)(155,159)(156,160)(161,178)(162,177)(163,179)(164,180)
(165,182)(166,181)(167,183)(168,184)(169,190)(170,189)(171,191)(172,192)
(173,186)(174,185)(175,187)(176,188)(193,242)(194,241)(195,243)(196,244)
(197,246)(198,245)(199,247)(200,248)(201,254)(202,253)(203,255)(204,256)
(205,250)(206,249)(207,251)(208,252)(209,274)(210,273)(211,275)(212,276)
(213,278)(214,277)(215,279)(216,280)(217,286)(218,285)(219,287)(220,288)
(221,282)(222,281)(223,283)(224,284)(225,258)(226,257)(227,259)(228,260)
(229,262)(230,261)(231,263)(232,264)(233,270)(234,269)(235,271)(236,272)
(237,266)(238,265)(239,267)(240,268);;
s3 := ( 1,161)( 2,162)( 3,163)( 4,164)( 5,173)( 6,174)( 7,175)( 8,176)
( 9,169)( 10,170)( 11,171)( 12,172)( 13,165)( 14,166)( 15,167)( 16,168)
( 17,145)( 18,146)( 19,147)( 20,148)( 21,157)( 22,158)( 23,159)( 24,160)
( 25,153)( 26,154)( 27,155)( 28,156)( 29,149)( 30,150)( 31,151)( 32,152)
( 33,177)( 34,178)( 35,179)( 36,180)( 37,189)( 38,190)( 39,191)( 40,192)
( 41,185)( 42,186)( 43,187)( 44,188)( 45,181)( 46,182)( 47,183)( 48,184)
( 49,209)( 50,210)( 51,211)( 52,212)( 53,221)( 54,222)( 55,223)( 56,224)
( 57,217)( 58,218)( 59,219)( 60,220)( 61,213)( 62,214)( 63,215)( 64,216)
( 65,193)( 66,194)( 67,195)( 68,196)( 69,205)( 70,206)( 71,207)( 72,208)
( 73,201)( 74,202)( 75,203)( 76,204)( 77,197)( 78,198)( 79,199)( 80,200)
( 81,225)( 82,226)( 83,227)( 84,228)( 85,237)( 86,238)( 87,239)( 88,240)
( 89,233)( 90,234)( 91,235)( 92,236)( 93,229)( 94,230)( 95,231)( 96,232)
( 97,257)( 98,258)( 99,259)(100,260)(101,269)(102,270)(103,271)(104,272)
(105,265)(106,266)(107,267)(108,268)(109,261)(110,262)(111,263)(112,264)
(113,241)(114,242)(115,243)(116,244)(117,253)(118,254)(119,255)(120,256)
(121,249)(122,250)(123,251)(124,252)(125,245)(126,246)(127,247)(128,248)
(129,273)(130,274)(131,275)(132,276)(133,285)(134,286)(135,287)(136,288)
(137,281)(138,282)(139,283)(140,284)(141,277)(142,278)(143,279)(144,280);;
s4 := ( 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,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s3*s4*s3*s4*s3*s4*s3*s4,
s4*s3*s2*s4*s3*s4*s3*s2*s3, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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, 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);
s2 := Sym(288)!( 1, 2)( 5, 6)( 9, 14)( 10, 13)( 11, 15)( 12, 16)( 17, 34)
( 18, 33)( 19, 35)( 20, 36)( 21, 38)( 22, 37)( 23, 39)( 24, 40)( 25, 46)
( 26, 45)( 27, 47)( 28, 48)( 29, 42)( 30, 41)( 31, 43)( 32, 44)( 49, 98)
( 50, 97)( 51, 99)( 52,100)( 53,102)( 54,101)( 55,103)( 56,104)( 57,110)
( 58,109)( 59,111)( 60,112)( 61,106)( 62,105)( 63,107)( 64,108)( 65,130)
( 66,129)( 67,131)( 68,132)( 69,134)( 70,133)( 71,135)( 72,136)( 73,142)
( 74,141)( 75,143)( 76,144)( 77,138)( 78,137)( 79,139)( 80,140)( 81,114)
( 82,113)( 83,115)( 84,116)( 85,118)( 86,117)( 87,119)( 88,120)( 89,126)
( 90,125)( 91,127)( 92,128)( 93,122)( 94,121)( 95,123)( 96,124)(145,146)
(149,150)(153,158)(154,157)(155,159)(156,160)(161,178)(162,177)(163,179)
(164,180)(165,182)(166,181)(167,183)(168,184)(169,190)(170,189)(171,191)
(172,192)(173,186)(174,185)(175,187)(176,188)(193,242)(194,241)(195,243)
(196,244)(197,246)(198,245)(199,247)(200,248)(201,254)(202,253)(203,255)
(204,256)(205,250)(206,249)(207,251)(208,252)(209,274)(210,273)(211,275)
(212,276)(213,278)(214,277)(215,279)(216,280)(217,286)(218,285)(219,287)
(220,288)(221,282)(222,281)(223,283)(224,284)(225,258)(226,257)(227,259)
(228,260)(229,262)(230,261)(231,263)(232,264)(233,270)(234,269)(235,271)
(236,272)(237,266)(238,265)(239,267)(240,268);
s3 := Sym(288)!( 1,161)( 2,162)( 3,163)( 4,164)( 5,173)( 6,174)( 7,175)
( 8,176)( 9,169)( 10,170)( 11,171)( 12,172)( 13,165)( 14,166)( 15,167)
( 16,168)( 17,145)( 18,146)( 19,147)( 20,148)( 21,157)( 22,158)( 23,159)
( 24,160)( 25,153)( 26,154)( 27,155)( 28,156)( 29,149)( 30,150)( 31,151)
( 32,152)( 33,177)( 34,178)( 35,179)( 36,180)( 37,189)( 38,190)( 39,191)
( 40,192)( 41,185)( 42,186)( 43,187)( 44,188)( 45,181)( 46,182)( 47,183)
( 48,184)( 49,209)( 50,210)( 51,211)( 52,212)( 53,221)( 54,222)( 55,223)
( 56,224)( 57,217)( 58,218)( 59,219)( 60,220)( 61,213)( 62,214)( 63,215)
( 64,216)( 65,193)( 66,194)( 67,195)( 68,196)( 69,205)( 70,206)( 71,207)
( 72,208)( 73,201)( 74,202)( 75,203)( 76,204)( 77,197)( 78,198)( 79,199)
( 80,200)( 81,225)( 82,226)( 83,227)( 84,228)( 85,237)( 86,238)( 87,239)
( 88,240)( 89,233)( 90,234)( 91,235)( 92,236)( 93,229)( 94,230)( 95,231)
( 96,232)( 97,257)( 98,258)( 99,259)(100,260)(101,269)(102,270)(103,271)
(104,272)(105,265)(106,266)(107,267)(108,268)(109,261)(110,262)(111,263)
(112,264)(113,241)(114,242)(115,243)(116,244)(117,253)(118,254)(119,255)
(120,256)(121,249)(122,250)(123,251)(124,252)(125,245)(126,246)(127,247)
(128,248)(129,273)(130,274)(131,275)(132,276)(133,285)(134,286)(135,287)
(136,288)(137,281)(138,282)(139,283)(140,284)(141,277)(142,278)(143,279)
(144,280);
s4 := 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,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s3*s4*s3*s4*s3*s4*s3*s4, s4*s3*s2*s4*s3*s4*s3*s2*s3,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope