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