Polytope of Type {24,4,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,4,3}*1152
Also Known As : {{24,4|2},{4,3}}. if this polytope has another name.
Group : SmallGroup(1152,155812)
Rank : 4
Schlafli Type : {24,4,3}
Number of vertices, edges, etc : 24, 96, 12, 6
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
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 : {12,4,3}*576
3-fold quotients : {8,4,3}*384
4-fold quotients : {24,2,3}*288, {6,4,3}*288
6-fold quotients : {4,4,3}*192b
8-fold quotients : {12,2,3}*144
12-fold quotients : {8,2,3}*96, {2,4,3}*96
16-fold quotients : {6,2,3}*72
24-fold quotients : {4,2,3}*48, {2,4,3}*48
32-fold quotients : {3,2,3}*36
48-fold quotients : {2,2,3}*24
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)
( 73,109)( 74,110)( 75,111)( 76,112)( 77,117)( 78,118)( 79,119)( 80,120)
( 81,113)( 82,114)( 83,115)( 84,116)( 85,121)( 86,122)( 87,123)( 88,124)
( 89,129)( 90,130)( 91,131)( 92,132)( 93,125)( 94,126)( 95,127)( 96,128)
( 97,133)( 98,134)( 99,135)(100,136)(101,141)(102,142)(103,143)(104,144)
(105,137)(106,138)(107,139)(108,140)(145,217)(146,218)(147,219)(148,220)
(149,225)(150,226)(151,227)(152,228)(153,221)(154,222)(155,223)(156,224)
(157,229)(158,230)(159,231)(160,232)(161,237)(162,238)(163,239)(164,240)
(165,233)(166,234)(167,235)(168,236)(169,241)(170,242)(171,243)(172,244)
(173,249)(174,250)(175,251)(176,252)(177,245)(178,246)(179,247)(180,248)
(181,253)(182,254)(183,255)(184,256)(185,261)(186,262)(187,263)(188,264)
(189,257)(190,258)(191,259)(192,260)(193,265)(194,266)(195,267)(196,268)
(197,273)(198,274)(199,275)(200,276)(201,269)(202,270)(203,271)(204,272)
(205,277)(206,278)(207,279)(208,280)(209,285)(210,286)(211,287)(212,288)
(213,281)(214,282)(215,283)(216,284);;
s1 := ( 1,151)( 2,152)( 3,149)( 4,150)( 5,147)( 6,148)( 7,145)( 8,146)
( 9,155)( 10,156)( 11,153)( 12,154)( 13,163)( 14,164)( 15,161)( 16,162)
( 17,159)( 18,160)( 19,157)( 20,158)( 21,167)( 22,168)( 23,165)( 24,166)
( 25,175)( 26,176)( 27,173)( 28,174)( 29,171)( 30,172)( 31,169)( 32,170)
( 33,179)( 34,180)( 35,177)( 36,178)( 37,187)( 38,188)( 39,185)( 40,186)
( 41,183)( 42,184)( 43,181)( 44,182)( 45,191)( 46,192)( 47,189)( 48,190)
( 49,199)( 50,200)( 51,197)( 52,198)( 53,195)( 54,196)( 55,193)( 56,194)
( 57,203)( 58,204)( 59,201)( 60,202)( 61,211)( 62,212)( 63,209)( 64,210)
( 65,207)( 66,208)( 67,205)( 68,206)( 69,215)( 70,216)( 71,213)( 72,214)
( 73,259)( 74,260)( 75,257)( 76,258)( 77,255)( 78,256)( 79,253)( 80,254)
( 81,263)( 82,264)( 83,261)( 84,262)( 85,271)( 86,272)( 87,269)( 88,270)
( 89,267)( 90,268)( 91,265)( 92,266)( 93,275)( 94,276)( 95,273)( 96,274)
( 97,283)( 98,284)( 99,281)(100,282)(101,279)(102,280)(103,277)(104,278)
(105,287)(106,288)(107,285)(108,286)(109,223)(110,224)(111,221)(112,222)
(113,219)(114,220)(115,217)(116,218)(117,227)(118,228)(119,225)(120,226)
(121,235)(122,236)(123,233)(124,234)(125,231)(126,232)(127,229)(128,230)
(129,239)(130,240)(131,237)(132,238)(133,247)(134,248)(135,245)(136,246)
(137,243)(138,244)(139,241)(140,242)(141,251)(142,252)(143,249)(144,250);;
s2 := ( 3, 4)( 7, 8)( 11, 12)( 13, 25)( 14, 26)( 15, 28)( 16, 27)( 17, 29)
( 18, 30)( 19, 32)( 20, 31)( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 39, 40)
( 43, 44)( 47, 48)( 49, 61)( 50, 62)( 51, 64)( 52, 63)( 53, 65)( 54, 66)
( 55, 68)( 56, 67)( 57, 69)( 58, 70)( 59, 72)( 60, 71)( 75, 76)( 79, 80)
( 83, 84)( 85, 97)( 86, 98)( 87,100)( 88, 99)( 89,101)( 90,102)( 91,104)
( 92,103)( 93,105)( 94,106)( 95,108)( 96,107)(111,112)(115,116)(119,120)
(121,133)(122,134)(123,136)(124,135)(125,137)(126,138)(127,140)(128,139)
(129,141)(130,142)(131,144)(132,143)(147,148)(151,152)(155,156)(157,169)
(158,170)(159,172)(160,171)(161,173)(162,174)(163,176)(164,175)(165,177)
(166,178)(167,180)(168,179)(183,184)(187,188)(191,192)(193,205)(194,206)
(195,208)(196,207)(197,209)(198,210)(199,212)(200,211)(201,213)(202,214)
(203,216)(204,215)(219,220)(223,224)(227,228)(229,241)(230,242)(231,244)
(232,243)(233,245)(234,246)(235,248)(236,247)(237,249)(238,250)(239,252)
(240,251)(255,256)(259,260)(263,264)(265,277)(266,278)(267,280)(268,279)
(269,281)(270,282)(271,284)(272,283)(273,285)(274,286)(275,288)(276,287);;
s3 := ( 1, 13)( 2, 16)( 3, 15)( 4, 14)( 5, 17)( 6, 20)( 7, 19)( 8, 18)
( 9, 21)( 10, 24)( 11, 23)( 12, 22)( 26, 28)( 30, 32)( 34, 36)( 37, 49)
( 38, 52)( 39, 51)( 40, 50)( 41, 53)( 42, 56)( 43, 55)( 44, 54)( 45, 57)
( 46, 60)( 47, 59)( 48, 58)( 62, 64)( 66, 68)( 70, 72)( 73, 85)( 74, 88)
( 75, 87)( 76, 86)( 77, 89)( 78, 92)( 79, 91)( 80, 90)( 81, 93)( 82, 96)
( 83, 95)( 84, 94)( 98,100)(102,104)(106,108)(109,121)(110,124)(111,123)
(112,122)(113,125)(114,128)(115,127)(116,126)(117,129)(118,132)(119,131)
(120,130)(134,136)(138,140)(142,144)(145,157)(146,160)(147,159)(148,158)
(149,161)(150,164)(151,163)(152,162)(153,165)(154,168)(155,167)(156,166)
(170,172)(174,176)(178,180)(181,193)(182,196)(183,195)(184,194)(185,197)
(186,200)(187,199)(188,198)(189,201)(190,204)(191,203)(192,202)(206,208)
(210,212)(214,216)(217,229)(218,232)(219,231)(220,230)(221,233)(222,236)
(223,235)(224,234)(225,237)(226,240)(227,239)(228,238)(242,244)(246,248)
(250,252)(253,265)(254,268)(255,267)(256,266)(257,269)(258,272)(259,271)
(260,270)(261,273)(262,276)(263,275)(264,274)(278,280)(282,284)(286,288);;
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,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
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)( 73,109)( 74,110)( 75,111)( 76,112)( 77,117)( 78,118)( 79,119)
( 80,120)( 81,113)( 82,114)( 83,115)( 84,116)( 85,121)( 86,122)( 87,123)
( 88,124)( 89,129)( 90,130)( 91,131)( 92,132)( 93,125)( 94,126)( 95,127)
( 96,128)( 97,133)( 98,134)( 99,135)(100,136)(101,141)(102,142)(103,143)
(104,144)(105,137)(106,138)(107,139)(108,140)(145,217)(146,218)(147,219)
(148,220)(149,225)(150,226)(151,227)(152,228)(153,221)(154,222)(155,223)
(156,224)(157,229)(158,230)(159,231)(160,232)(161,237)(162,238)(163,239)
(164,240)(165,233)(166,234)(167,235)(168,236)(169,241)(170,242)(171,243)
(172,244)(173,249)(174,250)(175,251)(176,252)(177,245)(178,246)(179,247)
(180,248)(181,253)(182,254)(183,255)(184,256)(185,261)(186,262)(187,263)
(188,264)(189,257)(190,258)(191,259)(192,260)(193,265)(194,266)(195,267)
(196,268)(197,273)(198,274)(199,275)(200,276)(201,269)(202,270)(203,271)
(204,272)(205,277)(206,278)(207,279)(208,280)(209,285)(210,286)(211,287)
(212,288)(213,281)(214,282)(215,283)(216,284);
s1 := Sym(288)!( 1,151)( 2,152)( 3,149)( 4,150)( 5,147)( 6,148)( 7,145)
( 8,146)( 9,155)( 10,156)( 11,153)( 12,154)( 13,163)( 14,164)( 15,161)
( 16,162)( 17,159)( 18,160)( 19,157)( 20,158)( 21,167)( 22,168)( 23,165)
( 24,166)( 25,175)( 26,176)( 27,173)( 28,174)( 29,171)( 30,172)( 31,169)
( 32,170)( 33,179)( 34,180)( 35,177)( 36,178)( 37,187)( 38,188)( 39,185)
( 40,186)( 41,183)( 42,184)( 43,181)( 44,182)( 45,191)( 46,192)( 47,189)
( 48,190)( 49,199)( 50,200)( 51,197)( 52,198)( 53,195)( 54,196)( 55,193)
( 56,194)( 57,203)( 58,204)( 59,201)( 60,202)( 61,211)( 62,212)( 63,209)
( 64,210)( 65,207)( 66,208)( 67,205)( 68,206)( 69,215)( 70,216)( 71,213)
( 72,214)( 73,259)( 74,260)( 75,257)( 76,258)( 77,255)( 78,256)( 79,253)
( 80,254)( 81,263)( 82,264)( 83,261)( 84,262)( 85,271)( 86,272)( 87,269)
( 88,270)( 89,267)( 90,268)( 91,265)( 92,266)( 93,275)( 94,276)( 95,273)
( 96,274)( 97,283)( 98,284)( 99,281)(100,282)(101,279)(102,280)(103,277)
(104,278)(105,287)(106,288)(107,285)(108,286)(109,223)(110,224)(111,221)
(112,222)(113,219)(114,220)(115,217)(116,218)(117,227)(118,228)(119,225)
(120,226)(121,235)(122,236)(123,233)(124,234)(125,231)(126,232)(127,229)
(128,230)(129,239)(130,240)(131,237)(132,238)(133,247)(134,248)(135,245)
(136,246)(137,243)(138,244)(139,241)(140,242)(141,251)(142,252)(143,249)
(144,250);
s2 := Sym(288)!( 3, 4)( 7, 8)( 11, 12)( 13, 25)( 14, 26)( 15, 28)( 16, 27)
( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 33)( 22, 34)( 23, 36)( 24, 35)
( 39, 40)( 43, 44)( 47, 48)( 49, 61)( 50, 62)( 51, 64)( 52, 63)( 53, 65)
( 54, 66)( 55, 68)( 56, 67)( 57, 69)( 58, 70)( 59, 72)( 60, 71)( 75, 76)
( 79, 80)( 83, 84)( 85, 97)( 86, 98)( 87,100)( 88, 99)( 89,101)( 90,102)
( 91,104)( 92,103)( 93,105)( 94,106)( 95,108)( 96,107)(111,112)(115,116)
(119,120)(121,133)(122,134)(123,136)(124,135)(125,137)(126,138)(127,140)
(128,139)(129,141)(130,142)(131,144)(132,143)(147,148)(151,152)(155,156)
(157,169)(158,170)(159,172)(160,171)(161,173)(162,174)(163,176)(164,175)
(165,177)(166,178)(167,180)(168,179)(183,184)(187,188)(191,192)(193,205)
(194,206)(195,208)(196,207)(197,209)(198,210)(199,212)(200,211)(201,213)
(202,214)(203,216)(204,215)(219,220)(223,224)(227,228)(229,241)(230,242)
(231,244)(232,243)(233,245)(234,246)(235,248)(236,247)(237,249)(238,250)
(239,252)(240,251)(255,256)(259,260)(263,264)(265,277)(266,278)(267,280)
(268,279)(269,281)(270,282)(271,284)(272,283)(273,285)(274,286)(275,288)
(276,287);
s3 := Sym(288)!( 1, 13)( 2, 16)( 3, 15)( 4, 14)( 5, 17)( 6, 20)( 7, 19)
( 8, 18)( 9, 21)( 10, 24)( 11, 23)( 12, 22)( 26, 28)( 30, 32)( 34, 36)
( 37, 49)( 38, 52)( 39, 51)( 40, 50)( 41, 53)( 42, 56)( 43, 55)( 44, 54)
( 45, 57)( 46, 60)( 47, 59)( 48, 58)( 62, 64)( 66, 68)( 70, 72)( 73, 85)
( 74, 88)( 75, 87)( 76, 86)( 77, 89)( 78, 92)( 79, 91)( 80, 90)( 81, 93)
( 82, 96)( 83, 95)( 84, 94)( 98,100)(102,104)(106,108)(109,121)(110,124)
(111,123)(112,122)(113,125)(114,128)(115,127)(116,126)(117,129)(118,132)
(119,131)(120,130)(134,136)(138,140)(142,144)(145,157)(146,160)(147,159)
(148,158)(149,161)(150,164)(151,163)(152,162)(153,165)(154,168)(155,167)
(156,166)(170,172)(174,176)(178,180)(181,193)(182,196)(183,195)(184,194)
(185,197)(186,200)(187,199)(188,198)(189,201)(190,204)(191,203)(192,202)
(206,208)(210,212)(214,216)(217,229)(218,232)(219,231)(220,230)(221,233)
(222,236)(223,235)(224,234)(225,237)(226,240)(227,239)(228,238)(242,244)
(246,248)(250,252)(253,265)(254,268)(255,267)(256,266)(257,269)(258,272)
(259,271)(260,270)(261,273)(262,276)(263,275)(264,274)(278,280)(282,284)
(286,288);
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, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope