Polytope of Type {6,4,3,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,3,4}*1152
Also Known As : {{6,4|2},{4,3},{3,4}3}. if this polytope has another name.
Group : SmallGroup(1152,157864)
Rank : 5
Schlafli Type : {6,4,3,4}
Number of vertices, edges, etc : 6, 24, 12, 12, 4
Order of s0s1s2s3s4 : 6
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) :
3-fold quotients : {2,4,3,4}*384b
4-fold quotients : {6,2,3,4}*288
6-fold quotients : {2,4,3,4}*192
8-fold quotients : {3,2,3,4}*144
12-fold quotients : {2,2,3,4}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 17, 33)( 18, 34)( 19, 35)( 20, 36)( 21, 37)( 22, 38)( 23, 39)( 24, 40)
( 25, 41)( 26, 42)( 27, 43)( 28, 44)( 29, 45)( 30, 46)( 31, 47)( 32, 48)
( 65, 81)( 66, 82)( 67, 83)( 68, 84)( 69, 85)( 70, 86)( 71, 87)( 72, 88)
( 73, 89)( 74, 90)( 75, 91)( 76, 92)( 77, 93)( 78, 94)( 79, 95)( 80, 96)
(113,129)(114,130)(115,131)(116,132)(117,133)(118,134)(119,135)(120,136)
(121,137)(122,138)(123,139)(124,140)(125,141)(126,142)(127,143)(128,144)
(161,177)(162,178)(163,179)(164,180)(165,181)(166,182)(167,183)(168,184)
(169,185)(170,186)(171,187)(172,188)(173,189)(174,190)(175,191)(176,192)
(209,225)(210,226)(211,227)(212,228)(213,229)(214,230)(215,231)(216,232)
(217,233)(218,234)(219,235)(220,236)(221,237)(222,238)(223,239)(224,240)
(257,273)(258,274)(259,275)(260,276)(261,277)(262,278)(263,279)(264,280)
(265,281)(266,282)(267,283)(268,284)(269,285)(270,286)(271,287)(272,288);;
s1 := ( 1,169)( 2,170)( 3,171)( 4,172)( 5,173)( 6,174)( 7,175)( 8,176)
( 9,161)( 10,162)( 11,163)( 12,164)( 13,165)( 14,166)( 15,167)( 16,168)
( 17,153)( 18,154)( 19,155)( 20,156)( 21,157)( 22,158)( 23,159)( 24,160)
( 25,145)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,151)( 32,152)
( 33,185)( 34,186)( 35,187)( 36,188)( 37,189)( 38,190)( 39,191)( 40,192)
( 41,177)( 42,178)( 43,179)( 44,180)( 45,181)( 46,182)( 47,183)( 48,184)
( 49,217)( 50,218)( 51,219)( 52,220)( 53,221)( 54,222)( 55,223)( 56,224)
( 57,209)( 58,210)( 59,211)( 60,212)( 61,213)( 62,214)( 63,215)( 64,216)
( 65,201)( 66,202)( 67,203)( 68,204)( 69,205)( 70,206)( 71,207)( 72,208)
( 73,193)( 74,194)( 75,195)( 76,196)( 77,197)( 78,198)( 79,199)( 80,200)
( 81,233)( 82,234)( 83,235)( 84,236)( 85,237)( 86,238)( 87,239)( 88,240)
( 89,225)( 90,226)( 91,227)( 92,228)( 93,229)( 94,230)( 95,231)( 96,232)
( 97,265)( 98,266)( 99,267)(100,268)(101,269)(102,270)(103,271)(104,272)
(105,257)(106,258)(107,259)(108,260)(109,261)(110,262)(111,263)(112,264)
(113,249)(114,250)(115,251)(116,252)(117,253)(118,254)(119,255)(120,256)
(121,241)(122,242)(123,243)(124,244)(125,245)(126,246)(127,247)(128,248)
(129,281)(130,282)(131,283)(132,284)(133,285)(134,286)(135,287)(136,288)
(137,273)(138,274)(139,275)(140,276)(141,277)(142,278)(143,279)(144,280);;
s2 := ( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 19, 20)( 23, 24)
( 25, 29)( 26, 30)( 27, 32)( 28, 31)( 35, 36)( 39, 40)( 41, 45)( 42, 46)
( 43, 48)( 44, 47)( 49, 97)( 50, 98)( 51,100)( 52, 99)( 53,101)( 54,102)
( 55,104)( 56,103)( 57,109)( 58,110)( 59,112)( 60,111)( 61,105)( 62,106)
( 63,108)( 64,107)( 65,113)( 66,114)( 67,116)( 68,115)( 69,117)( 70,118)
( 71,120)( 72,119)( 73,125)( 74,126)( 75,128)( 76,127)( 77,121)( 78,122)
( 79,124)( 80,123)( 81,129)( 82,130)( 83,132)( 84,131)( 85,133)( 86,134)
( 87,136)( 88,135)( 89,141)( 90,142)( 91,144)( 92,143)( 93,137)( 94,138)
( 95,140)( 96,139)(147,148)(151,152)(153,157)(154,158)(155,160)(156,159)
(163,164)(167,168)(169,173)(170,174)(171,176)(172,175)(179,180)(183,184)
(185,189)(186,190)(187,192)(188,191)(193,241)(194,242)(195,244)(196,243)
(197,245)(198,246)(199,248)(200,247)(201,253)(202,254)(203,256)(204,255)
(205,249)(206,250)(207,252)(208,251)(209,257)(210,258)(211,260)(212,259)
(213,261)(214,262)(215,264)(216,263)(217,269)(218,270)(219,272)(220,271)
(221,265)(222,266)(223,268)(224,267)(225,273)(226,274)(227,276)(228,275)
(229,277)(230,278)(231,280)(232,279)(233,285)(234,286)(235,288)(236,287)
(237,281)(238,282)(239,284)(240,283);;
s3 := ( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 61)( 6, 64)( 7, 63)( 8, 62)
( 9, 57)( 10, 60)( 11, 59)( 12, 58)( 13, 53)( 14, 56)( 15, 55)( 16, 54)
( 17, 65)( 18, 68)( 19, 67)( 20, 66)( 21, 77)( 22, 80)( 23, 79)( 24, 78)
( 25, 73)( 26, 76)( 27, 75)( 28, 74)( 29, 69)( 30, 72)( 31, 71)( 32, 70)
( 33, 81)( 34, 84)( 35, 83)( 36, 82)( 37, 93)( 38, 96)( 39, 95)( 40, 94)
( 41, 89)( 42, 92)( 43, 91)( 44, 90)( 45, 85)( 46, 88)( 47, 87)( 48, 86)
( 98,100)(101,109)(102,112)(103,111)(104,110)(106,108)(114,116)(117,125)
(118,128)(119,127)(120,126)(122,124)(130,132)(133,141)(134,144)(135,143)
(136,142)(138,140)(145,193)(146,196)(147,195)(148,194)(149,205)(150,208)
(151,207)(152,206)(153,201)(154,204)(155,203)(156,202)(157,197)(158,200)
(159,199)(160,198)(161,209)(162,212)(163,211)(164,210)(165,221)(166,224)
(167,223)(168,222)(169,217)(170,220)(171,219)(172,218)(173,213)(174,216)
(175,215)(176,214)(177,225)(178,228)(179,227)(180,226)(181,237)(182,240)
(183,239)(184,238)(185,233)(186,236)(187,235)(188,234)(189,229)(190,232)
(191,231)(192,230)(242,244)(245,253)(246,256)(247,255)(248,254)(250,252)
(258,260)(261,269)(262,272)(263,271)(264,270)(266,268)(274,276)(277,285)
(278,288)(279,287)(280,286)(282,284);;
s4 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)
(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)
(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)
(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)
(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)
(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288);;
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, s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s4*s3*s2*s4*s3*s2*s4*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(288)!( 17, 33)( 18, 34)( 19, 35)( 20, 36)( 21, 37)( 22, 38)( 23, 39)
( 24, 40)( 25, 41)( 26, 42)( 27, 43)( 28, 44)( 29, 45)( 30, 46)( 31, 47)
( 32, 48)( 65, 81)( 66, 82)( 67, 83)( 68, 84)( 69, 85)( 70, 86)( 71, 87)
( 72, 88)( 73, 89)( 74, 90)( 75, 91)( 76, 92)( 77, 93)( 78, 94)( 79, 95)
( 80, 96)(113,129)(114,130)(115,131)(116,132)(117,133)(118,134)(119,135)
(120,136)(121,137)(122,138)(123,139)(124,140)(125,141)(126,142)(127,143)
(128,144)(161,177)(162,178)(163,179)(164,180)(165,181)(166,182)(167,183)
(168,184)(169,185)(170,186)(171,187)(172,188)(173,189)(174,190)(175,191)
(176,192)(209,225)(210,226)(211,227)(212,228)(213,229)(214,230)(215,231)
(216,232)(217,233)(218,234)(219,235)(220,236)(221,237)(222,238)(223,239)
(224,240)(257,273)(258,274)(259,275)(260,276)(261,277)(262,278)(263,279)
(264,280)(265,281)(266,282)(267,283)(268,284)(269,285)(270,286)(271,287)
(272,288);
s1 := Sym(288)!( 1,169)( 2,170)( 3,171)( 4,172)( 5,173)( 6,174)( 7,175)
( 8,176)( 9,161)( 10,162)( 11,163)( 12,164)( 13,165)( 14,166)( 15,167)
( 16,168)( 17,153)( 18,154)( 19,155)( 20,156)( 21,157)( 22,158)( 23,159)
( 24,160)( 25,145)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,151)
( 32,152)( 33,185)( 34,186)( 35,187)( 36,188)( 37,189)( 38,190)( 39,191)
( 40,192)( 41,177)( 42,178)( 43,179)( 44,180)( 45,181)( 46,182)( 47,183)
( 48,184)( 49,217)( 50,218)( 51,219)( 52,220)( 53,221)( 54,222)( 55,223)
( 56,224)( 57,209)( 58,210)( 59,211)( 60,212)( 61,213)( 62,214)( 63,215)
( 64,216)( 65,201)( 66,202)( 67,203)( 68,204)( 69,205)( 70,206)( 71,207)
( 72,208)( 73,193)( 74,194)( 75,195)( 76,196)( 77,197)( 78,198)( 79,199)
( 80,200)( 81,233)( 82,234)( 83,235)( 84,236)( 85,237)( 86,238)( 87,239)
( 88,240)( 89,225)( 90,226)( 91,227)( 92,228)( 93,229)( 94,230)( 95,231)
( 96,232)( 97,265)( 98,266)( 99,267)(100,268)(101,269)(102,270)(103,271)
(104,272)(105,257)(106,258)(107,259)(108,260)(109,261)(110,262)(111,263)
(112,264)(113,249)(114,250)(115,251)(116,252)(117,253)(118,254)(119,255)
(120,256)(121,241)(122,242)(123,243)(124,244)(125,245)(126,246)(127,247)
(128,248)(129,281)(130,282)(131,283)(132,284)(133,285)(134,286)(135,287)
(136,288)(137,273)(138,274)(139,275)(140,276)(141,277)(142,278)(143,279)
(144,280);
s2 := Sym(288)!( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 19, 20)
( 23, 24)( 25, 29)( 26, 30)( 27, 32)( 28, 31)( 35, 36)( 39, 40)( 41, 45)
( 42, 46)( 43, 48)( 44, 47)( 49, 97)( 50, 98)( 51,100)( 52, 99)( 53,101)
( 54,102)( 55,104)( 56,103)( 57,109)( 58,110)( 59,112)( 60,111)( 61,105)
( 62,106)( 63,108)( 64,107)( 65,113)( 66,114)( 67,116)( 68,115)( 69,117)
( 70,118)( 71,120)( 72,119)( 73,125)( 74,126)( 75,128)( 76,127)( 77,121)
( 78,122)( 79,124)( 80,123)( 81,129)( 82,130)( 83,132)( 84,131)( 85,133)
( 86,134)( 87,136)( 88,135)( 89,141)( 90,142)( 91,144)( 92,143)( 93,137)
( 94,138)( 95,140)( 96,139)(147,148)(151,152)(153,157)(154,158)(155,160)
(156,159)(163,164)(167,168)(169,173)(170,174)(171,176)(172,175)(179,180)
(183,184)(185,189)(186,190)(187,192)(188,191)(193,241)(194,242)(195,244)
(196,243)(197,245)(198,246)(199,248)(200,247)(201,253)(202,254)(203,256)
(204,255)(205,249)(206,250)(207,252)(208,251)(209,257)(210,258)(211,260)
(212,259)(213,261)(214,262)(215,264)(216,263)(217,269)(218,270)(219,272)
(220,271)(221,265)(222,266)(223,268)(224,267)(225,273)(226,274)(227,276)
(228,275)(229,277)(230,278)(231,280)(232,279)(233,285)(234,286)(235,288)
(236,287)(237,281)(238,282)(239,284)(240,283);
s3 := Sym(288)!( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 61)( 6, 64)( 7, 63)
( 8, 62)( 9, 57)( 10, 60)( 11, 59)( 12, 58)( 13, 53)( 14, 56)( 15, 55)
( 16, 54)( 17, 65)( 18, 68)( 19, 67)( 20, 66)( 21, 77)( 22, 80)( 23, 79)
( 24, 78)( 25, 73)( 26, 76)( 27, 75)( 28, 74)( 29, 69)( 30, 72)( 31, 71)
( 32, 70)( 33, 81)( 34, 84)( 35, 83)( 36, 82)( 37, 93)( 38, 96)( 39, 95)
( 40, 94)( 41, 89)( 42, 92)( 43, 91)( 44, 90)( 45, 85)( 46, 88)( 47, 87)
( 48, 86)( 98,100)(101,109)(102,112)(103,111)(104,110)(106,108)(114,116)
(117,125)(118,128)(119,127)(120,126)(122,124)(130,132)(133,141)(134,144)
(135,143)(136,142)(138,140)(145,193)(146,196)(147,195)(148,194)(149,205)
(150,208)(151,207)(152,206)(153,201)(154,204)(155,203)(156,202)(157,197)
(158,200)(159,199)(160,198)(161,209)(162,212)(163,211)(164,210)(165,221)
(166,224)(167,223)(168,222)(169,217)(170,220)(171,219)(172,218)(173,213)
(174,216)(175,215)(176,214)(177,225)(178,228)(179,227)(180,226)(181,237)
(182,240)(183,239)(184,238)(185,233)(186,236)(187,235)(188,234)(189,229)
(190,232)(191,231)(192,230)(242,244)(245,253)(246,256)(247,255)(248,254)
(250,252)(258,260)(261,269)(262,272)(263,271)(264,270)(266,268)(274,276)
(277,285)(278,288)(279,287)(280,286)(282,284);
s4 := Sym(288)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)
(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)
(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)
(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)
(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)
(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)
(287,288);
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, s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s4*s3*s2*s4*s3*s2*s4*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope