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Polytope of Type {24,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,12}*1152s
if this polytope has a name.
Group : SmallGroup(1152,155849)
Rank : 3
Schlafli Type : {24,12}
Number of vertices, edges, etc : 48, 288, 24
Order of s0s1s2 : 6
Order of s0s1s2s1 : 24
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}*576h
   3-fold quotients : {24,4}*384f
   4-fold quotients : {6,12}*288b
   6-fold quotients : {12,4}*192c
   8-fold quotients : {3,12}*144
   12-fold quotients : {6,4}*96
   16-fold quotients : {6,6}*72c
   24-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
   32-fold quotients : {3,6}*36
   48-fold quotients : {3,4}*24, {6,2}*24
   96-fold quotients : {3,2}*12
   144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,145)(  2,146)(  3,148)(  4,147)(  5,151)(  6,152)(  7,149)(  8,150)
(  9,161)( 10,162)( 11,164)( 12,163)( 13,167)( 14,168)( 15,165)( 16,166)
( 17,153)( 18,154)( 19,156)( 20,155)( 21,159)( 22,160)( 23,157)( 24,158)
( 25,193)( 26,194)( 27,196)( 28,195)( 29,199)( 30,200)( 31,197)( 32,198)
( 33,209)( 34,210)( 35,212)( 36,211)( 37,215)( 38,216)( 39,213)( 40,214)
( 41,201)( 42,202)( 43,204)( 44,203)( 45,207)( 46,208)( 47,205)( 48,206)
( 49,169)( 50,170)( 51,172)( 52,171)( 53,175)( 54,176)( 55,173)( 56,174)
( 57,185)( 58,186)( 59,188)( 60,187)( 61,191)( 62,192)( 63,189)( 64,190)
( 65,177)( 66,178)( 67,180)( 68,179)( 69,183)( 70,184)( 71,181)( 72,182)
( 73,218)( 74,217)( 75,219)( 76,220)( 77,224)( 78,223)( 79,222)( 80,221)
( 81,234)( 82,233)( 83,235)( 84,236)( 85,240)( 86,239)( 87,238)( 88,237)
( 89,226)( 90,225)( 91,227)( 92,228)( 93,232)( 94,231)( 95,230)( 96,229)
( 97,266)( 98,265)( 99,267)(100,268)(101,272)(102,271)(103,270)(104,269)
(105,282)(106,281)(107,283)(108,284)(109,288)(110,287)(111,286)(112,285)
(113,274)(114,273)(115,275)(116,276)(117,280)(118,279)(119,278)(120,277)
(121,242)(122,241)(123,243)(124,244)(125,248)(126,247)(127,246)(128,245)
(129,258)(130,257)(131,259)(132,260)(133,264)(134,263)(135,262)(136,261)
(137,250)(138,249)(139,251)(140,252)(141,256)(142,255)(143,254)(144,253);;
s1 := (  1, 33)(  2, 34)(  3, 39)(  4, 40)(  5, 38)(  6, 37)(  7, 35)(  8, 36)
(  9, 25)( 10, 26)( 11, 31)( 12, 32)( 13, 30)( 14, 29)( 15, 27)( 16, 28)
( 17, 41)( 18, 42)( 19, 47)( 20, 48)( 21, 46)( 22, 45)( 23, 43)( 24, 44)
( 49, 57)( 50, 58)( 51, 63)( 52, 64)( 53, 62)( 54, 61)( 55, 59)( 56, 60)
( 67, 71)( 68, 72)( 69, 70)( 73,106)( 74,105)( 75,112)( 76,111)( 77,109)
( 78,110)( 79,108)( 80,107)( 81, 98)( 82, 97)( 83,104)( 84,103)( 85,101)
( 86,102)( 87,100)( 88, 99)( 89,114)( 90,113)( 91,120)( 92,119)( 93,117)
( 94,118)( 95,116)( 96,115)(121,130)(122,129)(123,136)(124,135)(125,133)
(126,134)(127,132)(128,131)(137,138)(139,144)(140,143)(145,250)(146,249)
(147,256)(148,255)(149,253)(150,254)(151,252)(152,251)(153,242)(154,241)
(155,248)(156,247)(157,245)(158,246)(159,244)(160,243)(161,258)(162,257)
(163,264)(164,263)(165,261)(166,262)(167,260)(168,259)(169,226)(170,225)
(171,232)(172,231)(173,229)(174,230)(175,228)(176,227)(177,218)(178,217)
(179,224)(180,223)(181,221)(182,222)(183,220)(184,219)(185,234)(186,233)
(187,240)(188,239)(189,237)(190,238)(191,236)(192,235)(193,274)(194,273)
(195,280)(196,279)(197,277)(198,278)(199,276)(200,275)(201,266)(202,265)
(203,272)(204,271)(205,269)(206,270)(207,268)(208,267)(209,282)(210,281)
(211,288)(212,287)(213,285)(214,286)(215,284)(216,283);;
s2 := (  1,147)(  2,148)(  3,146)(  4,145)(  5,151)(  6,152)(  7,150)(  8,149)
(  9,163)( 10,164)( 11,162)( 12,161)( 13,167)( 14,168)( 15,166)( 16,165)
( 17,155)( 18,156)( 19,154)( 20,153)( 21,159)( 22,160)( 23,158)( 24,157)
( 25,171)( 26,172)( 27,170)( 28,169)( 29,175)( 30,176)( 31,174)( 32,173)
( 33,187)( 34,188)( 35,186)( 36,185)( 37,191)( 38,192)( 39,190)( 40,189)
( 41,179)( 42,180)( 43,178)( 44,177)( 45,183)( 46,184)( 47,182)( 48,181)
( 49,195)( 50,196)( 51,194)( 52,193)( 53,199)( 54,200)( 55,198)( 56,197)
( 57,211)( 58,212)( 59,210)( 60,209)( 61,215)( 62,216)( 63,214)( 64,213)
( 65,203)( 66,204)( 67,202)( 68,201)( 69,207)( 70,208)( 71,206)( 72,205)
( 73,220)( 74,219)( 75,217)( 76,218)( 77,224)( 78,223)( 79,221)( 80,222)
( 81,236)( 82,235)( 83,233)( 84,234)( 85,240)( 86,239)( 87,237)( 88,238)
( 89,228)( 90,227)( 91,225)( 92,226)( 93,232)( 94,231)( 95,229)( 96,230)
( 97,244)( 98,243)( 99,241)(100,242)(101,248)(102,247)(103,245)(104,246)
(105,260)(106,259)(107,257)(108,258)(109,264)(110,263)(111,261)(112,262)
(113,252)(114,251)(115,249)(116,250)(117,256)(118,255)(119,253)(120,254)
(121,268)(122,267)(123,265)(124,266)(125,272)(126,271)(127,269)(128,270)
(129,284)(130,283)(131,281)(132,282)(133,288)(134,287)(135,285)(136,286)
(137,276)(138,275)(139,273)(140,274)(141,280)(142,279)(143,277)(144,278);;
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*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1, 
s2*s1*s0*s1*s0*s1*s2*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)!(  1,145)(  2,146)(  3,148)(  4,147)(  5,151)(  6,152)(  7,149)
(  8,150)(  9,161)( 10,162)( 11,164)( 12,163)( 13,167)( 14,168)( 15,165)
( 16,166)( 17,153)( 18,154)( 19,156)( 20,155)( 21,159)( 22,160)( 23,157)
( 24,158)( 25,193)( 26,194)( 27,196)( 28,195)( 29,199)( 30,200)( 31,197)
( 32,198)( 33,209)( 34,210)( 35,212)( 36,211)( 37,215)( 38,216)( 39,213)
( 40,214)( 41,201)( 42,202)( 43,204)( 44,203)( 45,207)( 46,208)( 47,205)
( 48,206)( 49,169)( 50,170)( 51,172)( 52,171)( 53,175)( 54,176)( 55,173)
( 56,174)( 57,185)( 58,186)( 59,188)( 60,187)( 61,191)( 62,192)( 63,189)
( 64,190)( 65,177)( 66,178)( 67,180)( 68,179)( 69,183)( 70,184)( 71,181)
( 72,182)( 73,218)( 74,217)( 75,219)( 76,220)( 77,224)( 78,223)( 79,222)
( 80,221)( 81,234)( 82,233)( 83,235)( 84,236)( 85,240)( 86,239)( 87,238)
( 88,237)( 89,226)( 90,225)( 91,227)( 92,228)( 93,232)( 94,231)( 95,230)
( 96,229)( 97,266)( 98,265)( 99,267)(100,268)(101,272)(102,271)(103,270)
(104,269)(105,282)(106,281)(107,283)(108,284)(109,288)(110,287)(111,286)
(112,285)(113,274)(114,273)(115,275)(116,276)(117,280)(118,279)(119,278)
(120,277)(121,242)(122,241)(123,243)(124,244)(125,248)(126,247)(127,246)
(128,245)(129,258)(130,257)(131,259)(132,260)(133,264)(134,263)(135,262)
(136,261)(137,250)(138,249)(139,251)(140,252)(141,256)(142,255)(143,254)
(144,253);
s1 := Sym(288)!(  1, 33)(  2, 34)(  3, 39)(  4, 40)(  5, 38)(  6, 37)(  7, 35)
(  8, 36)(  9, 25)( 10, 26)( 11, 31)( 12, 32)( 13, 30)( 14, 29)( 15, 27)
( 16, 28)( 17, 41)( 18, 42)( 19, 47)( 20, 48)( 21, 46)( 22, 45)( 23, 43)
( 24, 44)( 49, 57)( 50, 58)( 51, 63)( 52, 64)( 53, 62)( 54, 61)( 55, 59)
( 56, 60)( 67, 71)( 68, 72)( 69, 70)( 73,106)( 74,105)( 75,112)( 76,111)
( 77,109)( 78,110)( 79,108)( 80,107)( 81, 98)( 82, 97)( 83,104)( 84,103)
( 85,101)( 86,102)( 87,100)( 88, 99)( 89,114)( 90,113)( 91,120)( 92,119)
( 93,117)( 94,118)( 95,116)( 96,115)(121,130)(122,129)(123,136)(124,135)
(125,133)(126,134)(127,132)(128,131)(137,138)(139,144)(140,143)(145,250)
(146,249)(147,256)(148,255)(149,253)(150,254)(151,252)(152,251)(153,242)
(154,241)(155,248)(156,247)(157,245)(158,246)(159,244)(160,243)(161,258)
(162,257)(163,264)(164,263)(165,261)(166,262)(167,260)(168,259)(169,226)
(170,225)(171,232)(172,231)(173,229)(174,230)(175,228)(176,227)(177,218)
(178,217)(179,224)(180,223)(181,221)(182,222)(183,220)(184,219)(185,234)
(186,233)(187,240)(188,239)(189,237)(190,238)(191,236)(192,235)(193,274)
(194,273)(195,280)(196,279)(197,277)(198,278)(199,276)(200,275)(201,266)
(202,265)(203,272)(204,271)(205,269)(206,270)(207,268)(208,267)(209,282)
(210,281)(211,288)(212,287)(213,285)(214,286)(215,284)(216,283);
s2 := Sym(288)!(  1,147)(  2,148)(  3,146)(  4,145)(  5,151)(  6,152)(  7,150)
(  8,149)(  9,163)( 10,164)( 11,162)( 12,161)( 13,167)( 14,168)( 15,166)
( 16,165)( 17,155)( 18,156)( 19,154)( 20,153)( 21,159)( 22,160)( 23,158)
( 24,157)( 25,171)( 26,172)( 27,170)( 28,169)( 29,175)( 30,176)( 31,174)
( 32,173)( 33,187)( 34,188)( 35,186)( 36,185)( 37,191)( 38,192)( 39,190)
( 40,189)( 41,179)( 42,180)( 43,178)( 44,177)( 45,183)( 46,184)( 47,182)
( 48,181)( 49,195)( 50,196)( 51,194)( 52,193)( 53,199)( 54,200)( 55,198)
( 56,197)( 57,211)( 58,212)( 59,210)( 60,209)( 61,215)( 62,216)( 63,214)
( 64,213)( 65,203)( 66,204)( 67,202)( 68,201)( 69,207)( 70,208)( 71,206)
( 72,205)( 73,220)( 74,219)( 75,217)( 76,218)( 77,224)( 78,223)( 79,221)
( 80,222)( 81,236)( 82,235)( 83,233)( 84,234)( 85,240)( 86,239)( 87,237)
( 88,238)( 89,228)( 90,227)( 91,225)( 92,226)( 93,232)( 94,231)( 95,229)
( 96,230)( 97,244)( 98,243)( 99,241)(100,242)(101,248)(102,247)(103,245)
(104,246)(105,260)(106,259)(107,257)(108,258)(109,264)(110,263)(111,261)
(112,262)(113,252)(114,251)(115,249)(116,250)(117,256)(118,255)(119,253)
(120,254)(121,268)(122,267)(123,265)(124,266)(125,272)(126,271)(127,269)
(128,270)(129,284)(130,283)(131,281)(132,282)(133,288)(134,287)(135,285)
(136,286)(137,276)(138,275)(139,273)(140,274)(141,280)(142,279)(143,277)
(144,278);
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*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1, 
s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope