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