Polytope of Type {6,24,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,24,4}*1152h
if this polytope has a name.
Group : SmallGroup(1152,155800)
Rank : 4
Schlafli Type : {6,24,4}
Number of vertices, edges, etc : 6, 72, 48, 4
Order of s0s1s2s3 : 24
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 : {6,12,4}*576d
3-fold quotients : {2,24,4}*384d
4-fold quotients : {6,6,4}*288d
6-fold quotients : {2,12,4}*192b
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 := ( 5, 9)( 6, 10)( 7, 11)( 8, 12)( 17, 21)( 18, 22)( 19, 23)( 20, 24)
( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 41, 45)( 42, 46)( 43, 47)( 44, 48)
( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 65, 69)( 66, 70)( 67, 71)( 68, 72)
( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 89, 93)( 90, 94)( 91, 95)( 92, 96)
(101,105)(102,106)(103,107)(104,108)(113,117)(114,118)(115,119)(116,120)
(125,129)(126,130)(127,131)(128,132)(137,141)(138,142)(139,143)(140,144)
(149,153)(150,154)(151,155)(152,156)(161,165)(162,166)(163,167)(164,168)
(173,177)(174,178)(175,179)(176,180)(185,189)(186,190)(187,191)(188,192)
(197,201)(198,202)(199,203)(200,204)(209,213)(210,214)(211,215)(212,216)
(221,225)(222,226)(223,227)(224,228)(233,237)(234,238)(235,239)(236,240)
(245,249)(246,250)(247,251)(248,252)(257,261)(258,262)(259,263)(260,264)
(269,273)(270,274)(271,275)(272,276)(281,285)(282,286)(283,287)(284,288);;
s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 11, 12)( 13, 29)( 14, 30)( 15, 32)
( 16, 31)( 17, 25)( 18, 26)( 19, 28)( 20, 27)( 21, 33)( 22, 34)( 23, 36)
( 24, 35)( 37, 41)( 38, 42)( 39, 44)( 40, 43)( 47, 48)( 49, 65)( 50, 66)
( 51, 68)( 52, 67)( 53, 61)( 54, 62)( 55, 64)( 56, 63)( 57, 69)( 58, 70)
( 59, 72)( 60, 71)( 73,113)( 74,114)( 75,116)( 76,115)( 77,109)( 78,110)
( 79,112)( 80,111)( 81,117)( 82,118)( 83,120)( 84,119)( 85,137)( 86,138)
( 87,140)( 88,139)( 89,133)( 90,134)( 91,136)( 92,135)( 93,141)( 94,142)
( 95,144)( 96,143)( 97,125)( 98,126)( 99,128)(100,127)(101,121)(102,122)
(103,124)(104,123)(105,129)(106,130)(107,132)(108,131)(145,221)(146,222)
(147,224)(148,223)(149,217)(150,218)(151,220)(152,219)(153,225)(154,226)
(155,228)(156,227)(157,245)(158,246)(159,248)(160,247)(161,241)(162,242)
(163,244)(164,243)(165,249)(166,250)(167,252)(168,251)(169,233)(170,234)
(171,236)(172,235)(173,229)(174,230)(175,232)(176,231)(177,237)(178,238)
(179,240)(180,239)(181,257)(182,258)(183,260)(184,259)(185,253)(186,254)
(187,256)(188,255)(189,261)(190,262)(191,264)(192,263)(193,281)(194,282)
(195,284)(196,283)(197,277)(198,278)(199,280)(200,279)(201,285)(202,286)
(203,288)(204,287)(205,269)(206,270)(207,272)(208,271)(209,265)(210,266)
(211,268)(212,267)(213,273)(214,274)(215,276)(216,275);;
s2 := ( 1,157)( 2,160)( 3,159)( 4,158)( 5,161)( 6,164)( 7,163)( 8,162)
( 9,165)( 10,168)( 11,167)( 12,166)( 13,145)( 14,148)( 15,147)( 16,146)
( 17,149)( 18,152)( 19,151)( 20,150)( 21,153)( 22,156)( 23,155)( 24,154)
( 25,169)( 26,172)( 27,171)( 28,170)( 29,173)( 30,176)( 31,175)( 32,174)
( 33,177)( 34,180)( 35,179)( 36,178)( 37,193)( 38,196)( 39,195)( 40,194)
( 41,197)( 42,200)( 43,199)( 44,198)( 45,201)( 46,204)( 47,203)( 48,202)
( 49,181)( 50,184)( 51,183)( 52,182)( 53,185)( 54,188)( 55,187)( 56,186)
( 57,189)( 58,192)( 59,191)( 60,190)( 61,205)( 62,208)( 63,207)( 64,206)
( 65,209)( 66,212)( 67,211)( 68,210)( 69,213)( 70,216)( 71,215)( 72,214)
( 73,265)( 74,268)( 75,267)( 76,266)( 77,269)( 78,272)( 79,271)( 80,270)
( 81,273)( 82,276)( 83,275)( 84,274)( 85,253)( 86,256)( 87,255)( 88,254)
( 89,257)( 90,260)( 91,259)( 92,258)( 93,261)( 94,264)( 95,263)( 96,262)
( 97,277)( 98,280)( 99,279)(100,278)(101,281)(102,284)(103,283)(104,282)
(105,285)(106,288)(107,287)(108,286)(109,229)(110,232)(111,231)(112,230)
(113,233)(114,236)(115,235)(116,234)(117,237)(118,240)(119,239)(120,238)
(121,217)(122,220)(123,219)(124,218)(125,221)(126,224)(127,223)(128,222)
(129,225)(130,228)(131,227)(132,226)(133,241)(134,244)(135,243)(136,242)
(137,245)(138,248)(139,247)(140,246)(141,249)(142,252)(143,251)(144,250);;
s3 := ( 1, 38)( 2, 37)( 3, 40)( 4, 39)( 5, 42)( 6, 41)( 7, 44)( 8, 43)
( 9, 46)( 10, 45)( 11, 48)( 12, 47)( 13, 50)( 14, 49)( 15, 52)( 16, 51)
( 17, 54)( 18, 53)( 19, 56)( 20, 55)( 21, 58)( 22, 57)( 23, 60)( 24, 59)
( 25, 62)( 26, 61)( 27, 64)( 28, 63)( 29, 66)( 30, 65)( 31, 68)( 32, 67)
( 33, 70)( 34, 69)( 35, 72)( 36, 71)( 73,110)( 74,109)( 75,112)( 76,111)
( 77,114)( 78,113)( 79,116)( 80,115)( 81,118)( 82,117)( 83,120)( 84,119)
( 85,122)( 86,121)( 87,124)( 88,123)( 89,126)( 90,125)( 91,128)( 92,127)
( 93,130)( 94,129)( 95,132)( 96,131)( 97,134)( 98,133)( 99,136)(100,135)
(101,138)(102,137)(103,140)(104,139)(105,142)(106,141)(107,144)(108,143)
(145,182)(146,181)(147,184)(148,183)(149,186)(150,185)(151,188)(152,187)
(153,190)(154,189)(155,192)(156,191)(157,194)(158,193)(159,196)(160,195)
(161,198)(162,197)(163,200)(164,199)(165,202)(166,201)(167,204)(168,203)
(169,206)(170,205)(171,208)(172,207)(173,210)(174,209)(175,212)(176,211)
(177,214)(178,213)(179,216)(180,215)(217,254)(218,253)(219,256)(220,255)
(221,258)(222,257)(223,260)(224,259)(225,262)(226,261)(227,264)(228,263)
(229,266)(230,265)(231,268)(232,267)(233,270)(234,269)(235,272)(236,271)
(237,274)(238,273)(239,276)(240,275)(241,278)(242,277)(243,280)(244,279)
(245,282)(246,281)(247,284)(248,283)(249,286)(250,285)(251,288)(252,287);;
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, s0*s1*s2*s1*s0*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(288)!( 5, 9)( 6, 10)( 7, 11)( 8, 12)( 17, 21)( 18, 22)( 19, 23)
( 20, 24)( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 41, 45)( 42, 46)( 43, 47)
( 44, 48)( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 65, 69)( 66, 70)( 67, 71)
( 68, 72)( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 89, 93)( 90, 94)( 91, 95)
( 92, 96)(101,105)(102,106)(103,107)(104,108)(113,117)(114,118)(115,119)
(116,120)(125,129)(126,130)(127,131)(128,132)(137,141)(138,142)(139,143)
(140,144)(149,153)(150,154)(151,155)(152,156)(161,165)(162,166)(163,167)
(164,168)(173,177)(174,178)(175,179)(176,180)(185,189)(186,190)(187,191)
(188,192)(197,201)(198,202)(199,203)(200,204)(209,213)(210,214)(211,215)
(212,216)(221,225)(222,226)(223,227)(224,228)(233,237)(234,238)(235,239)
(236,240)(245,249)(246,250)(247,251)(248,252)(257,261)(258,262)(259,263)
(260,264)(269,273)(270,274)(271,275)(272,276)(281,285)(282,286)(283,287)
(284,288);
s1 := Sym(288)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 11, 12)( 13, 29)( 14, 30)
( 15, 32)( 16, 31)( 17, 25)( 18, 26)( 19, 28)( 20, 27)( 21, 33)( 22, 34)
( 23, 36)( 24, 35)( 37, 41)( 38, 42)( 39, 44)( 40, 43)( 47, 48)( 49, 65)
( 50, 66)( 51, 68)( 52, 67)( 53, 61)( 54, 62)( 55, 64)( 56, 63)( 57, 69)
( 58, 70)( 59, 72)( 60, 71)( 73,113)( 74,114)( 75,116)( 76,115)( 77,109)
( 78,110)( 79,112)( 80,111)( 81,117)( 82,118)( 83,120)( 84,119)( 85,137)
( 86,138)( 87,140)( 88,139)( 89,133)( 90,134)( 91,136)( 92,135)( 93,141)
( 94,142)( 95,144)( 96,143)( 97,125)( 98,126)( 99,128)(100,127)(101,121)
(102,122)(103,124)(104,123)(105,129)(106,130)(107,132)(108,131)(145,221)
(146,222)(147,224)(148,223)(149,217)(150,218)(151,220)(152,219)(153,225)
(154,226)(155,228)(156,227)(157,245)(158,246)(159,248)(160,247)(161,241)
(162,242)(163,244)(164,243)(165,249)(166,250)(167,252)(168,251)(169,233)
(170,234)(171,236)(172,235)(173,229)(174,230)(175,232)(176,231)(177,237)
(178,238)(179,240)(180,239)(181,257)(182,258)(183,260)(184,259)(185,253)
(186,254)(187,256)(188,255)(189,261)(190,262)(191,264)(192,263)(193,281)
(194,282)(195,284)(196,283)(197,277)(198,278)(199,280)(200,279)(201,285)
(202,286)(203,288)(204,287)(205,269)(206,270)(207,272)(208,271)(209,265)
(210,266)(211,268)(212,267)(213,273)(214,274)(215,276)(216,275);
s2 := Sym(288)!( 1,157)( 2,160)( 3,159)( 4,158)( 5,161)( 6,164)( 7,163)
( 8,162)( 9,165)( 10,168)( 11,167)( 12,166)( 13,145)( 14,148)( 15,147)
( 16,146)( 17,149)( 18,152)( 19,151)( 20,150)( 21,153)( 22,156)( 23,155)
( 24,154)( 25,169)( 26,172)( 27,171)( 28,170)( 29,173)( 30,176)( 31,175)
( 32,174)( 33,177)( 34,180)( 35,179)( 36,178)( 37,193)( 38,196)( 39,195)
( 40,194)( 41,197)( 42,200)( 43,199)( 44,198)( 45,201)( 46,204)( 47,203)
( 48,202)( 49,181)( 50,184)( 51,183)( 52,182)( 53,185)( 54,188)( 55,187)
( 56,186)( 57,189)( 58,192)( 59,191)( 60,190)( 61,205)( 62,208)( 63,207)
( 64,206)( 65,209)( 66,212)( 67,211)( 68,210)( 69,213)( 70,216)( 71,215)
( 72,214)( 73,265)( 74,268)( 75,267)( 76,266)( 77,269)( 78,272)( 79,271)
( 80,270)( 81,273)( 82,276)( 83,275)( 84,274)( 85,253)( 86,256)( 87,255)
( 88,254)( 89,257)( 90,260)( 91,259)( 92,258)( 93,261)( 94,264)( 95,263)
( 96,262)( 97,277)( 98,280)( 99,279)(100,278)(101,281)(102,284)(103,283)
(104,282)(105,285)(106,288)(107,287)(108,286)(109,229)(110,232)(111,231)
(112,230)(113,233)(114,236)(115,235)(116,234)(117,237)(118,240)(119,239)
(120,238)(121,217)(122,220)(123,219)(124,218)(125,221)(126,224)(127,223)
(128,222)(129,225)(130,228)(131,227)(132,226)(133,241)(134,244)(135,243)
(136,242)(137,245)(138,248)(139,247)(140,246)(141,249)(142,252)(143,251)
(144,250);
s3 := Sym(288)!( 1, 38)( 2, 37)( 3, 40)( 4, 39)( 5, 42)( 6, 41)( 7, 44)
( 8, 43)( 9, 46)( 10, 45)( 11, 48)( 12, 47)( 13, 50)( 14, 49)( 15, 52)
( 16, 51)( 17, 54)( 18, 53)( 19, 56)( 20, 55)( 21, 58)( 22, 57)( 23, 60)
( 24, 59)( 25, 62)( 26, 61)( 27, 64)( 28, 63)( 29, 66)( 30, 65)( 31, 68)
( 32, 67)( 33, 70)( 34, 69)( 35, 72)( 36, 71)( 73,110)( 74,109)( 75,112)
( 76,111)( 77,114)( 78,113)( 79,116)( 80,115)( 81,118)( 82,117)( 83,120)
( 84,119)( 85,122)( 86,121)( 87,124)( 88,123)( 89,126)( 90,125)( 91,128)
( 92,127)( 93,130)( 94,129)( 95,132)( 96,131)( 97,134)( 98,133)( 99,136)
(100,135)(101,138)(102,137)(103,140)(104,139)(105,142)(106,141)(107,144)
(108,143)(145,182)(146,181)(147,184)(148,183)(149,186)(150,185)(151,188)
(152,187)(153,190)(154,189)(155,192)(156,191)(157,194)(158,193)(159,196)
(160,195)(161,198)(162,197)(163,200)(164,199)(165,202)(166,201)(167,204)
(168,203)(169,206)(170,205)(171,208)(172,207)(173,210)(174,209)(175,212)
(176,211)(177,214)(178,213)(179,216)(180,215)(217,254)(218,253)(219,256)
(220,255)(221,258)(222,257)(223,260)(224,259)(225,262)(226,261)(227,264)
(228,263)(229,266)(230,265)(231,268)(232,267)(233,270)(234,269)(235,272)
(236,271)(237,274)(238,273)(239,276)(240,275)(241,278)(242,277)(243,280)
(244,279)(245,282)(246,281)(247,284)(248,283)(249,286)(250,285)(251,288)
(252,287);
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,
s0*s1*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope