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Polytope of Type {12,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,24}*1152n
if this polytope has a name.
Group : SmallGroup(1152,155788)
Rank : 3
Schlafli Type : {12,24}
Number of vertices, edges, etc : 24, 288, 48
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, {6,24}*576d
   3-fold quotients : {12,8}*384g
   4-fold quotients : {6,12}*288b
   6-fold quotients : {12,4}*192c, {6,8}*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)
( 73,217)( 74,218)( 75,220)( 76,219)( 77,223)( 78,224)( 79,221)( 80,222)
( 81,233)( 82,234)( 83,236)( 84,235)( 85,239)( 86,240)( 87,237)( 88,238)
( 89,225)( 90,226)( 91,228)( 92,227)( 93,231)( 94,232)( 95,229)( 96,230)
( 97,265)( 98,266)( 99,268)(100,267)(101,271)(102,272)(103,269)(104,270)
(105,281)(106,282)(107,284)(108,283)(109,287)(110,288)(111,285)(112,286)
(113,273)(114,274)(115,276)(116,275)(117,279)(118,280)(119,277)(120,278)
(121,241)(122,242)(123,244)(124,243)(125,247)(126,248)(127,245)(128,246)
(129,257)(130,258)(131,260)(132,259)(133,263)(134,264)(135,261)(136,262)
(137,249)(138,250)(139,252)(140,251)(141,255)(142,256)(143,253)(144,254);;
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)( 73,105)( 74,106)( 75,111)( 76,112)( 77,110)
( 78,109)( 79,107)( 80,108)( 81, 97)( 82, 98)( 83,103)( 84,104)( 85,102)
( 86,101)( 87, 99)( 88,100)( 89,113)( 90,114)( 91,119)( 92,120)( 93,118)
( 94,117)( 95,115)( 96,116)(121,129)(122,130)(123,135)(124,136)(125,134)
(126,133)(127,131)(128,132)(139,143)(140,144)(141,142)(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)
( 73,219)( 74,220)( 75,218)( 76,217)( 77,223)( 78,224)( 79,222)( 80,221)
( 81,235)( 82,236)( 83,234)( 84,233)( 85,239)( 86,240)( 87,238)( 88,237)
( 89,227)( 90,228)( 91,226)( 92,225)( 93,231)( 94,232)( 95,230)( 96,229)
( 97,243)( 98,244)( 99,242)(100,241)(101,247)(102,248)(103,246)(104,245)
(105,259)(106,260)(107,258)(108,257)(109,263)(110,264)(111,262)(112,261)
(113,251)(114,252)(115,250)(116,249)(117,255)(118,256)(119,254)(120,253)
(121,267)(122,268)(123,266)(124,265)(125,271)(126,272)(127,270)(128,269)
(129,283)(130,284)(131,282)(132,281)(133,287)(134,288)(135,286)(136,285)
(137,275)(138,276)(139,274)(140,273)(141,279)(142,280)(143,278)(144,277);;
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, 
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)!(  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)( 73,217)( 74,218)( 75,220)( 76,219)( 77,223)( 78,224)( 79,221)
( 80,222)( 81,233)( 82,234)( 83,236)( 84,235)( 85,239)( 86,240)( 87,237)
( 88,238)( 89,225)( 90,226)( 91,228)( 92,227)( 93,231)( 94,232)( 95,229)
( 96,230)( 97,265)( 98,266)( 99,268)(100,267)(101,271)(102,272)(103,269)
(104,270)(105,281)(106,282)(107,284)(108,283)(109,287)(110,288)(111,285)
(112,286)(113,273)(114,274)(115,276)(116,275)(117,279)(118,280)(119,277)
(120,278)(121,241)(122,242)(123,244)(124,243)(125,247)(126,248)(127,245)
(128,246)(129,257)(130,258)(131,260)(132,259)(133,263)(134,264)(135,261)
(136,262)(137,249)(138,250)(139,252)(140,251)(141,255)(142,256)(143,253)
(144,254);
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)( 73,105)( 74,106)( 75,111)( 76,112)
( 77,110)( 78,109)( 79,107)( 80,108)( 81, 97)( 82, 98)( 83,103)( 84,104)
( 85,102)( 86,101)( 87, 99)( 88,100)( 89,113)( 90,114)( 91,119)( 92,120)
( 93,118)( 94,117)( 95,115)( 96,116)(121,129)(122,130)(123,135)(124,136)
(125,134)(126,133)(127,131)(128,132)(139,143)(140,144)(141,142)(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)( 73,219)( 74,220)( 75,218)( 76,217)( 77,223)( 78,224)( 79,222)
( 80,221)( 81,235)( 82,236)( 83,234)( 84,233)( 85,239)( 86,240)( 87,238)
( 88,237)( 89,227)( 90,228)( 91,226)( 92,225)( 93,231)( 94,232)( 95,230)
( 96,229)( 97,243)( 98,244)( 99,242)(100,241)(101,247)(102,248)(103,246)
(104,245)(105,259)(106,260)(107,258)(108,257)(109,263)(110,264)(111,262)
(112,261)(113,251)(114,252)(115,250)(116,249)(117,255)(118,256)(119,254)
(120,253)(121,267)(122,268)(123,266)(124,265)(125,271)(126,272)(127,270)
(128,269)(129,283)(130,284)(131,282)(132,281)(133,287)(134,288)(135,286)
(136,285)(137,275)(138,276)(139,274)(140,273)(141,279)(142,280)(143,278)
(144,277);
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, 
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