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Polytope of Type {24,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,6}*1152b
if this polytope has a name.
Group : SmallGroup(1152,155485)
Rank : 3
Schlafli Type : {24,6}
Number of vertices, edges, etc : 96, 288, 24
Order of s0s1s2 : 6
Order of s0s1s2s1 : 8
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 : {24,6}*576a
   3-fold quotients : {8,6}*384d
   4-fold quotients : {12,6}*288a
   6-fold quotients : {8,6}*192a
   8-fold quotients : {12,6}*144d
   12-fold quotients : {4,6}*96
   16-fold quotients : {6,6}*72a
   24-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   48-fold quotients : {4,3}*24, {2,6}*24, {6,2}*24
   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 := (  1,  9)(  2, 10)(  3, 11)(  4, 12)(  5, 14)(  6, 13)(  7, 16)(  8, 15)
( 17, 41)( 18, 42)( 19, 43)( 20, 44)( 21, 46)( 22, 45)( 23, 48)( 24, 47)
( 25, 33)( 26, 34)( 27, 35)( 28, 36)( 29, 38)( 30, 37)( 31, 40)( 32, 39)
( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 62)( 54, 61)( 55, 64)( 56, 63)
( 65, 89)( 66, 90)( 67, 91)( 68, 92)( 69, 94)( 70, 93)( 71, 96)( 72, 95)
( 73, 81)( 74, 82)( 75, 83)( 76, 84)( 77, 86)( 78, 85)( 79, 88)( 80, 87)
( 97,105)( 98,106)( 99,107)(100,108)(101,110)(102,109)(103,112)(104,111)
(113,137)(114,138)(115,139)(116,140)(117,142)(118,141)(119,144)(120,143)
(121,129)(122,130)(123,131)(124,132)(125,134)(126,133)(127,136)(128,135)
(145,153)(146,154)(147,155)(148,156)(149,158)(150,157)(151,160)(152,159)
(161,185)(162,186)(163,187)(164,188)(165,190)(166,189)(167,192)(168,191)
(169,177)(170,178)(171,179)(172,180)(173,182)(174,181)(175,184)(176,183)
(193,201)(194,202)(195,203)(196,204)(197,206)(198,205)(199,208)(200,207)
(209,233)(210,234)(211,235)(212,236)(213,238)(214,237)(215,240)(216,239)
(217,225)(218,226)(219,227)(220,228)(221,230)(222,229)(223,232)(224,231)
(241,249)(242,250)(243,251)(244,252)(245,254)(246,253)(247,256)(248,255)
(257,281)(258,282)(259,283)(260,284)(261,286)(262,285)(263,288)(264,287)
(265,273)(266,274)(267,275)(268,276)(269,278)(270,277)(271,280)(272,279);;
s1 := (  1, 17)(  2, 18)(  3, 20)(  4, 19)(  5, 21)(  6, 22)(  7, 24)(  8, 23)
(  9, 32)( 10, 31)( 11, 29)( 12, 30)( 13, 27)( 14, 28)( 15, 26)( 16, 25)
( 35, 36)( 39, 40)( 41, 48)( 42, 47)( 43, 45)( 44, 46)( 49,113)( 50,114)
( 51,116)( 52,115)( 53,117)( 54,118)( 55,120)( 56,119)( 57,128)( 58,127)
( 59,125)( 60,126)( 61,123)( 62,124)( 63,122)( 64,121)( 65, 97)( 66, 98)
( 67,100)( 68, 99)( 69,101)( 70,102)( 71,104)( 72,103)( 73,112)( 74,111)
( 75,109)( 76,110)( 77,107)( 78,108)( 79,106)( 80,105)( 81,129)( 82,130)
( 83,132)( 84,131)( 85,133)( 86,134)( 87,136)( 88,135)( 89,144)( 90,143)
( 91,141)( 92,142)( 93,139)( 94,140)( 95,138)( 96,137)(145,161)(146,162)
(147,164)(148,163)(149,165)(150,166)(151,168)(152,167)(153,176)(154,175)
(155,173)(156,174)(157,171)(158,172)(159,170)(160,169)(179,180)(183,184)
(185,192)(186,191)(187,189)(188,190)(193,257)(194,258)(195,260)(196,259)
(197,261)(198,262)(199,264)(200,263)(201,272)(202,271)(203,269)(204,270)
(205,267)(206,268)(207,266)(208,265)(209,241)(210,242)(211,244)(212,243)
(213,245)(214,246)(215,248)(216,247)(217,256)(218,255)(219,253)(220,254)
(221,251)(222,252)(223,250)(224,249)(225,273)(226,274)(227,276)(228,275)
(229,277)(230,278)(231,280)(232,279)(233,288)(234,287)(235,285)(236,286)
(237,283)(238,284)(239,282)(240,281);;
s2 := (  1,193)(  2,196)(  3,195)(  4,194)(  5,206)(  6,207)(  7,208)(  8,205)
(  9,201)( 10,204)( 11,203)( 12,202)( 13,200)( 14,197)( 15,198)( 16,199)
( 17,209)( 18,212)( 19,211)( 20,210)( 21,222)( 22,223)( 23,224)( 24,221)
( 25,217)( 26,220)( 27,219)( 28,218)( 29,216)( 30,213)( 31,214)( 32,215)
( 33,225)( 34,228)( 35,227)( 36,226)( 37,238)( 38,239)( 39,240)( 40,237)
( 41,233)( 42,236)( 43,235)( 44,234)( 45,232)( 46,229)( 47,230)( 48,231)
( 49,145)( 50,148)( 51,147)( 52,146)( 53,158)( 54,159)( 55,160)( 56,157)
( 57,153)( 58,156)( 59,155)( 60,154)( 61,152)( 62,149)( 63,150)( 64,151)
( 65,161)( 66,164)( 67,163)( 68,162)( 69,174)( 70,175)( 71,176)( 72,173)
( 73,169)( 74,172)( 75,171)( 76,170)( 77,168)( 78,165)( 79,166)( 80,167)
( 81,177)( 82,180)( 83,179)( 84,178)( 85,190)( 86,191)( 87,192)( 88,189)
( 89,185)( 90,188)( 91,187)( 92,186)( 93,184)( 94,181)( 95,182)( 96,183)
( 97,241)( 98,244)( 99,243)(100,242)(101,254)(102,255)(103,256)(104,253)
(105,249)(106,252)(107,251)(108,250)(109,248)(110,245)(111,246)(112,247)
(113,257)(114,260)(115,259)(116,258)(117,270)(118,271)(119,272)(120,269)
(121,265)(122,268)(123,267)(124,266)(125,264)(126,261)(127,262)(128,263)
(129,273)(130,276)(131,275)(132,274)(133,286)(134,287)(135,288)(136,285)
(137,281)(138,284)(139,283)(140,282)(141,280)(142,277)(143,278)(144,279);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(288)!(  1,  9)(  2, 10)(  3, 11)(  4, 12)(  5, 14)(  6, 13)(  7, 16)
(  8, 15)( 17, 41)( 18, 42)( 19, 43)( 20, 44)( 21, 46)( 22, 45)( 23, 48)
( 24, 47)( 25, 33)( 26, 34)( 27, 35)( 28, 36)( 29, 38)( 30, 37)( 31, 40)
( 32, 39)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 62)( 54, 61)( 55, 64)
( 56, 63)( 65, 89)( 66, 90)( 67, 91)( 68, 92)( 69, 94)( 70, 93)( 71, 96)
( 72, 95)( 73, 81)( 74, 82)( 75, 83)( 76, 84)( 77, 86)( 78, 85)( 79, 88)
( 80, 87)( 97,105)( 98,106)( 99,107)(100,108)(101,110)(102,109)(103,112)
(104,111)(113,137)(114,138)(115,139)(116,140)(117,142)(118,141)(119,144)
(120,143)(121,129)(122,130)(123,131)(124,132)(125,134)(126,133)(127,136)
(128,135)(145,153)(146,154)(147,155)(148,156)(149,158)(150,157)(151,160)
(152,159)(161,185)(162,186)(163,187)(164,188)(165,190)(166,189)(167,192)
(168,191)(169,177)(170,178)(171,179)(172,180)(173,182)(174,181)(175,184)
(176,183)(193,201)(194,202)(195,203)(196,204)(197,206)(198,205)(199,208)
(200,207)(209,233)(210,234)(211,235)(212,236)(213,238)(214,237)(215,240)
(216,239)(217,225)(218,226)(219,227)(220,228)(221,230)(222,229)(223,232)
(224,231)(241,249)(242,250)(243,251)(244,252)(245,254)(246,253)(247,256)
(248,255)(257,281)(258,282)(259,283)(260,284)(261,286)(262,285)(263,288)
(264,287)(265,273)(266,274)(267,275)(268,276)(269,278)(270,277)(271,280)
(272,279);
s1 := Sym(288)!(  1, 17)(  2, 18)(  3, 20)(  4, 19)(  5, 21)(  6, 22)(  7, 24)
(  8, 23)(  9, 32)( 10, 31)( 11, 29)( 12, 30)( 13, 27)( 14, 28)( 15, 26)
( 16, 25)( 35, 36)( 39, 40)( 41, 48)( 42, 47)( 43, 45)( 44, 46)( 49,113)
( 50,114)( 51,116)( 52,115)( 53,117)( 54,118)( 55,120)( 56,119)( 57,128)
( 58,127)( 59,125)( 60,126)( 61,123)( 62,124)( 63,122)( 64,121)( 65, 97)
( 66, 98)( 67,100)( 68, 99)( 69,101)( 70,102)( 71,104)( 72,103)( 73,112)
( 74,111)( 75,109)( 76,110)( 77,107)( 78,108)( 79,106)( 80,105)( 81,129)
( 82,130)( 83,132)( 84,131)( 85,133)( 86,134)( 87,136)( 88,135)( 89,144)
( 90,143)( 91,141)( 92,142)( 93,139)( 94,140)( 95,138)( 96,137)(145,161)
(146,162)(147,164)(148,163)(149,165)(150,166)(151,168)(152,167)(153,176)
(154,175)(155,173)(156,174)(157,171)(158,172)(159,170)(160,169)(179,180)
(183,184)(185,192)(186,191)(187,189)(188,190)(193,257)(194,258)(195,260)
(196,259)(197,261)(198,262)(199,264)(200,263)(201,272)(202,271)(203,269)
(204,270)(205,267)(206,268)(207,266)(208,265)(209,241)(210,242)(211,244)
(212,243)(213,245)(214,246)(215,248)(216,247)(217,256)(218,255)(219,253)
(220,254)(221,251)(222,252)(223,250)(224,249)(225,273)(226,274)(227,276)
(228,275)(229,277)(230,278)(231,280)(232,279)(233,288)(234,287)(235,285)
(236,286)(237,283)(238,284)(239,282)(240,281);
s2 := Sym(288)!(  1,193)(  2,196)(  3,195)(  4,194)(  5,206)(  6,207)(  7,208)
(  8,205)(  9,201)( 10,204)( 11,203)( 12,202)( 13,200)( 14,197)( 15,198)
( 16,199)( 17,209)( 18,212)( 19,211)( 20,210)( 21,222)( 22,223)( 23,224)
( 24,221)( 25,217)( 26,220)( 27,219)( 28,218)( 29,216)( 30,213)( 31,214)
( 32,215)( 33,225)( 34,228)( 35,227)( 36,226)( 37,238)( 38,239)( 39,240)
( 40,237)( 41,233)( 42,236)( 43,235)( 44,234)( 45,232)( 46,229)( 47,230)
( 48,231)( 49,145)( 50,148)( 51,147)( 52,146)( 53,158)( 54,159)( 55,160)
( 56,157)( 57,153)( 58,156)( 59,155)( 60,154)( 61,152)( 62,149)( 63,150)
( 64,151)( 65,161)( 66,164)( 67,163)( 68,162)( 69,174)( 70,175)( 71,176)
( 72,173)( 73,169)( 74,172)( 75,171)( 76,170)( 77,168)( 78,165)( 79,166)
( 80,167)( 81,177)( 82,180)( 83,179)( 84,178)( 85,190)( 86,191)( 87,192)
( 88,189)( 89,185)( 90,188)( 91,187)( 92,186)( 93,184)( 94,181)( 95,182)
( 96,183)( 97,241)( 98,244)( 99,243)(100,242)(101,254)(102,255)(103,256)
(104,253)(105,249)(106,252)(107,251)(108,250)(109,248)(110,245)(111,246)
(112,247)(113,257)(114,260)(115,259)(116,258)(117,270)(118,271)(119,272)
(120,269)(121,265)(122,268)(123,267)(124,266)(125,264)(126,261)(127,262)
(128,263)(129,273)(130,276)(131,275)(132,274)(133,286)(134,287)(135,288)
(136,285)(137,281)(138,284)(139,283)(140,282)(141,280)(142,277)(143,278)
(144,279);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope