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Polytope of Type {6,24}

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