Polytope of Type {24,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,12}*1152o
if this polytope has a name.
Group : SmallGroup(1152,155800)
Rank : 3
Schlafli Type : {24,12}
Number of vertices, edges, etc : 48, 288, 24
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,12}*576d
   3-fold quotients : {24,4}*384c
   4-fold quotients : {24,6}*288a, {6,12}*288a
   6-fold quotients : {24,4}*192c, {24,4}*192d, {12,4}*192b
   8-fold quotients : {12,6}*144a, {6,12}*144d
   12-fold quotients : {24,2}*96, {8,6}*96, {12,4}*96b, {12,4}*96c, {6,4}*96
   16-fold quotients : {6,6}*72a
   24-fold quotients : {12,2}*48, {4,6}*48a, {3,4}*48, {6,4}*48b, {6,4}*48c
   36-fold quotients : {8,2}*32
   48-fold quotients : {3,4}*24, {2,6}*24, {6,2}*24
   72-fold quotients : {4,2}*16
   96-fold quotients : {2,3}*12, {3,2}*12
   144-fold quotients : {2,2}*8
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)( 73,109)( 74,110)
( 75,112)( 76,111)( 77,113)( 78,114)( 79,116)( 80,115)( 81,117)( 82,118)
( 83,120)( 84,119)( 85,133)( 86,134)( 87,136)( 88,135)( 89,137)( 90,138)
( 91,140)( 92,139)( 93,141)( 94,142)( 95,144)( 96,143)( 97,121)( 98,122)
( 99,124)(100,123)(101,125)(102,126)(103,128)(104,127)(105,129)(106,130)
(107,132)(108,131)(145,217)(146,218)(147,220)(148,219)(149,221)(150,222)
(151,224)(152,223)(153,225)(154,226)(155,228)(156,227)(157,241)(158,242)
(159,244)(160,243)(161,245)(162,246)(163,248)(164,247)(165,249)(166,250)
(167,252)(168,251)(169,229)(170,230)(171,232)(172,231)(173,233)(174,234)
(175,236)(176,235)(177,237)(178,238)(179,240)(180,239)(181,253)(182,254)
(183,256)(184,255)(185,257)(186,258)(187,260)(188,259)(189,261)(190,262)
(191,264)(192,263)(193,277)(194,278)(195,280)(196,279)(197,281)(198,282)
(199,284)(200,283)(201,285)(202,286)(203,288)(204,287)(205,265)(206,266)
(207,268)(208,267)(209,269)(210,270)(211,272)(212,271)(213,273)(214,274)
(215,276)(216,275);;
s1 := (  1,157)(  2,160)(  3,159)(  4,158)(  5,165)(  6,168)(  7,167)(  8,166)
(  9,161)( 10,164)( 11,163)( 12,162)( 13,145)( 14,148)( 15,147)( 16,146)
( 17,153)( 18,156)( 19,155)( 20,154)( 21,149)( 22,152)( 23,151)( 24,150)
( 25,169)( 26,172)( 27,171)( 28,170)( 29,177)( 30,180)( 31,179)( 32,178)
( 33,173)( 34,176)( 35,175)( 36,174)( 37,193)( 38,196)( 39,195)( 40,194)
( 41,201)( 42,204)( 43,203)( 44,202)( 45,197)( 46,200)( 47,199)( 48,198)
( 49,181)( 50,184)( 51,183)( 52,182)( 53,189)( 54,192)( 55,191)( 56,190)
( 57,185)( 58,188)( 59,187)( 60,186)( 61,205)( 62,208)( 63,207)( 64,206)
( 65,213)( 66,216)( 67,215)( 68,214)( 69,209)( 70,212)( 71,211)( 72,210)
( 73,265)( 74,268)( 75,267)( 76,266)( 77,273)( 78,276)( 79,275)( 80,274)
( 81,269)( 82,272)( 83,271)( 84,270)( 85,253)( 86,256)( 87,255)( 88,254)
( 89,261)( 90,264)( 91,263)( 92,262)( 93,257)( 94,260)( 95,259)( 96,258)
( 97,277)( 98,280)( 99,279)(100,278)(101,285)(102,288)(103,287)(104,286)
(105,281)(106,284)(107,283)(108,282)(109,229)(110,232)(111,231)(112,230)
(113,237)(114,240)(115,239)(116,238)(117,233)(118,236)(119,235)(120,234)
(121,217)(122,220)(123,219)(124,218)(125,225)(126,228)(127,227)(128,226)
(129,221)(130,224)(131,223)(132,222)(133,241)(134,244)(135,243)(136,242)
(137,249)(138,252)(139,251)(140,250)(141,245)(142,248)(143,247)(144,246);;
s2 := (  1,  6)(  2,  5)(  3,  8)(  4,  7)(  9, 10)( 11, 12)( 13, 18)( 14, 17)
( 15, 20)( 16, 19)( 21, 22)( 23, 24)( 25, 30)( 26, 29)( 27, 32)( 28, 31)
( 33, 34)( 35, 36)( 37, 42)( 38, 41)( 39, 44)( 40, 43)( 45, 46)( 47, 48)
( 49, 54)( 50, 53)( 51, 56)( 52, 55)( 57, 58)( 59, 60)( 61, 66)( 62, 65)
( 63, 68)( 64, 67)( 69, 70)( 71, 72)( 73, 78)( 74, 77)( 75, 80)( 76, 79)
( 81, 82)( 83, 84)( 85, 90)( 86, 89)( 87, 92)( 88, 91)( 93, 94)( 95, 96)
( 97,102)( 98,101)( 99,104)(100,103)(105,106)(107,108)(109,114)(110,113)
(111,116)(112,115)(117,118)(119,120)(121,126)(122,125)(123,128)(124,127)
(129,130)(131,132)(133,138)(134,137)(135,140)(136,139)(141,142)(143,144)
(145,150)(146,149)(147,152)(148,151)(153,154)(155,156)(157,162)(158,161)
(159,164)(160,163)(165,166)(167,168)(169,174)(170,173)(171,176)(172,175)
(177,178)(179,180)(181,186)(182,185)(183,188)(184,187)(189,190)(191,192)
(193,198)(194,197)(195,200)(196,199)(201,202)(203,204)(205,210)(206,209)
(207,212)(208,211)(213,214)(215,216)(217,222)(218,221)(219,224)(220,223)
(225,226)(227,228)(229,234)(230,233)(231,236)(232,235)(237,238)(239,240)
(241,246)(242,245)(243,248)(244,247)(249,250)(251,252)(253,258)(254,257)
(255,260)(256,259)(261,262)(263,264)(265,270)(266,269)(267,272)(268,271)
(273,274)(275,276)(277,282)(278,281)(279,284)(280,283)(285,286)(287,288);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*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*s0*s1 ];;
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)( 73,109)
( 74,110)( 75,112)( 76,111)( 77,113)( 78,114)( 79,116)( 80,115)( 81,117)
( 82,118)( 83,120)( 84,119)( 85,133)( 86,134)( 87,136)( 88,135)( 89,137)
( 90,138)( 91,140)( 92,139)( 93,141)( 94,142)( 95,144)( 96,143)( 97,121)
( 98,122)( 99,124)(100,123)(101,125)(102,126)(103,128)(104,127)(105,129)
(106,130)(107,132)(108,131)(145,217)(146,218)(147,220)(148,219)(149,221)
(150,222)(151,224)(152,223)(153,225)(154,226)(155,228)(156,227)(157,241)
(158,242)(159,244)(160,243)(161,245)(162,246)(163,248)(164,247)(165,249)
(166,250)(167,252)(168,251)(169,229)(170,230)(171,232)(172,231)(173,233)
(174,234)(175,236)(176,235)(177,237)(178,238)(179,240)(180,239)(181,253)
(182,254)(183,256)(184,255)(185,257)(186,258)(187,260)(188,259)(189,261)
(190,262)(191,264)(192,263)(193,277)(194,278)(195,280)(196,279)(197,281)
(198,282)(199,284)(200,283)(201,285)(202,286)(203,288)(204,287)(205,265)
(206,266)(207,268)(208,267)(209,269)(210,270)(211,272)(212,271)(213,273)
(214,274)(215,276)(216,275);
s1 := Sym(288)!(  1,157)(  2,160)(  3,159)(  4,158)(  5,165)(  6,168)(  7,167)
(  8,166)(  9,161)( 10,164)( 11,163)( 12,162)( 13,145)( 14,148)( 15,147)
( 16,146)( 17,153)( 18,156)( 19,155)( 20,154)( 21,149)( 22,152)( 23,151)
( 24,150)( 25,169)( 26,172)( 27,171)( 28,170)( 29,177)( 30,180)( 31,179)
( 32,178)( 33,173)( 34,176)( 35,175)( 36,174)( 37,193)( 38,196)( 39,195)
( 40,194)( 41,201)( 42,204)( 43,203)( 44,202)( 45,197)( 46,200)( 47,199)
( 48,198)( 49,181)( 50,184)( 51,183)( 52,182)( 53,189)( 54,192)( 55,191)
( 56,190)( 57,185)( 58,188)( 59,187)( 60,186)( 61,205)( 62,208)( 63,207)
( 64,206)( 65,213)( 66,216)( 67,215)( 68,214)( 69,209)( 70,212)( 71,211)
( 72,210)( 73,265)( 74,268)( 75,267)( 76,266)( 77,273)( 78,276)( 79,275)
( 80,274)( 81,269)( 82,272)( 83,271)( 84,270)( 85,253)( 86,256)( 87,255)
( 88,254)( 89,261)( 90,264)( 91,263)( 92,262)( 93,257)( 94,260)( 95,259)
( 96,258)( 97,277)( 98,280)( 99,279)(100,278)(101,285)(102,288)(103,287)
(104,286)(105,281)(106,284)(107,283)(108,282)(109,229)(110,232)(111,231)
(112,230)(113,237)(114,240)(115,239)(116,238)(117,233)(118,236)(119,235)
(120,234)(121,217)(122,220)(123,219)(124,218)(125,225)(126,228)(127,227)
(128,226)(129,221)(130,224)(131,223)(132,222)(133,241)(134,244)(135,243)
(136,242)(137,249)(138,252)(139,251)(140,250)(141,245)(142,248)(143,247)
(144,246);
s2 := Sym(288)!(  1,  6)(  2,  5)(  3,  8)(  4,  7)(  9, 10)( 11, 12)( 13, 18)
( 14, 17)( 15, 20)( 16, 19)( 21, 22)( 23, 24)( 25, 30)( 26, 29)( 27, 32)
( 28, 31)( 33, 34)( 35, 36)( 37, 42)( 38, 41)( 39, 44)( 40, 43)( 45, 46)
( 47, 48)( 49, 54)( 50, 53)( 51, 56)( 52, 55)( 57, 58)( 59, 60)( 61, 66)
( 62, 65)( 63, 68)( 64, 67)( 69, 70)( 71, 72)( 73, 78)( 74, 77)( 75, 80)
( 76, 79)( 81, 82)( 83, 84)( 85, 90)( 86, 89)( 87, 92)( 88, 91)( 93, 94)
( 95, 96)( 97,102)( 98,101)( 99,104)(100,103)(105,106)(107,108)(109,114)
(110,113)(111,116)(112,115)(117,118)(119,120)(121,126)(122,125)(123,128)
(124,127)(129,130)(131,132)(133,138)(134,137)(135,140)(136,139)(141,142)
(143,144)(145,150)(146,149)(147,152)(148,151)(153,154)(155,156)(157,162)
(158,161)(159,164)(160,163)(165,166)(167,168)(169,174)(170,173)(171,176)
(172,175)(177,178)(179,180)(181,186)(182,185)(183,188)(184,187)(189,190)
(191,192)(193,198)(194,197)(195,200)(196,199)(201,202)(203,204)(205,210)
(206,209)(207,212)(208,211)(213,214)(215,216)(217,222)(218,221)(219,224)
(220,223)(225,226)(227,228)(229,234)(230,233)(231,236)(232,235)(237,238)
(239,240)(241,246)(242,245)(243,248)(244,247)(249,250)(251,252)(253,258)
(254,257)(255,260)(256,259)(261,262)(263,264)(265,270)(266,269)(267,272)
(268,271)(273,274)(275,276)(277,282)(278,281)(279,284)(280,283)(285,286)
(287,288);
poly := sub<Sym(288)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*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*s0*s1 >;

References : None.
to this polytope