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