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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}*1152n
if this polytope has a name.
Group : SmallGroup(1152,155788)
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}*576i, {24,6}*576d
   3-fold quotients : {8,12}*384g
   4-fold quotients : {12,6}*288b
   6-fold quotients : {4,12}*192c, {8,6}*192c
   8-fold quotients : {12,3}*144
   12-fold quotients : {4,6}*96
   16-fold quotients : {6,6}*72b
   24-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   32-fold quotients : {6,3}*36
   48-fold quotients : {4,3}*24, {2,6}*24
   96-fold quotients : {2,3}*12
   144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,149)(  2,150)(  3,152)(  4,151)(  5,146)(  6,145)(  7,147)(  8,148)
(  9,165)( 10,166)( 11,168)( 12,167)( 13,162)( 14,161)( 15,163)( 16,164)
( 17,157)( 18,158)( 19,160)( 20,159)( 21,154)( 22,153)( 23,155)( 24,156)
( 25,173)( 26,174)( 27,176)( 28,175)( 29,170)( 30,169)( 31,171)( 32,172)
( 33,189)( 34,190)( 35,192)( 36,191)( 37,186)( 38,185)( 39,187)( 40,188)
( 41,181)( 42,182)( 43,184)( 44,183)( 45,178)( 46,177)( 47,179)( 48,180)
( 49,197)( 50,198)( 51,200)( 52,199)( 53,194)( 54,193)( 55,195)( 56,196)
( 57,213)( 58,214)( 59,216)( 60,215)( 61,210)( 62,209)( 63,211)( 64,212)
( 65,205)( 66,206)( 67,208)( 68,207)( 69,202)( 70,201)( 71,203)( 72,204)
( 73,221)( 74,222)( 75,224)( 76,223)( 77,218)( 78,217)( 79,219)( 80,220)
( 81,237)( 82,238)( 83,240)( 84,239)( 85,234)( 86,233)( 87,235)( 88,236)
( 89,229)( 90,230)( 91,232)( 92,231)( 93,226)( 94,225)( 95,227)( 96,228)
( 97,245)( 98,246)( 99,248)(100,247)(101,242)(102,241)(103,243)(104,244)
(105,261)(106,262)(107,264)(108,263)(109,258)(110,257)(111,259)(112,260)
(113,253)(114,254)(115,256)(116,255)(117,250)(118,249)(119,251)(120,252)
(121,269)(122,270)(123,272)(124,271)(125,266)(126,265)(127,267)(128,268)
(129,285)(130,286)(131,288)(132,287)(133,282)(134,281)(135,283)(136,284)
(137,277)(138,278)(139,280)(140,279)(141,274)(142,273)(143,275)(144,276);;
s1 := (  1,  9)(  2, 10)(  3, 12)(  4, 11)(  5, 15)(  6, 16)(  7, 13)(  8, 14)
( 19, 20)( 21, 23)( 22, 24)( 25, 57)( 26, 58)( 27, 60)( 28, 59)( 29, 63)
( 30, 64)( 31, 61)( 32, 62)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 55)
( 38, 56)( 39, 53)( 40, 54)( 41, 65)( 42, 66)( 43, 68)( 44, 67)( 45, 71)
( 46, 72)( 47, 69)( 48, 70)( 73, 81)( 74, 82)( 75, 84)( 76, 83)( 77, 87)
( 78, 88)( 79, 85)( 80, 86)( 91, 92)( 93, 95)( 94, 96)( 97,129)( 98,130)
( 99,132)(100,131)(101,135)(102,136)(103,133)(104,134)(105,121)(106,122)
(107,124)(108,123)(109,127)(110,128)(111,125)(112,126)(113,137)(114,138)
(115,140)(116,139)(117,143)(118,144)(119,141)(120,142)(145,226)(146,225)
(147,227)(148,228)(149,232)(150,231)(151,230)(152,229)(153,218)(154,217)
(155,219)(156,220)(157,224)(158,223)(159,222)(160,221)(161,234)(162,233)
(163,235)(164,236)(165,240)(166,239)(167,238)(168,237)(169,274)(170,273)
(171,275)(172,276)(173,280)(174,279)(175,278)(176,277)(177,266)(178,265)
(179,267)(180,268)(181,272)(182,271)(183,270)(184,269)(185,282)(186,281)
(187,283)(188,284)(189,288)(190,287)(191,286)(192,285)(193,250)(194,249)
(195,251)(196,252)(197,256)(198,255)(199,254)(200,253)(201,242)(202,241)
(203,243)(204,244)(205,248)(206,247)(207,246)(208,245)(209,258)(210,257)
(211,259)(212,260)(213,264)(214,263)(215,262)(216,261);;
s2 := (  1,169)(  2,170)(  3,175)(  4,176)(  5,174)(  6,173)(  7,171)(  8,172)
(  9,185)( 10,186)( 11,191)( 12,192)( 13,190)( 14,189)( 15,187)( 16,188)
( 17,177)( 18,178)( 19,183)( 20,184)( 21,182)( 22,181)( 23,179)( 24,180)
( 25,145)( 26,146)( 27,151)( 28,152)( 29,150)( 30,149)( 31,147)( 32,148)
( 33,161)( 34,162)( 35,167)( 36,168)( 37,166)( 38,165)( 39,163)( 40,164)
( 41,153)( 42,154)( 43,159)( 44,160)( 45,158)( 46,157)( 47,155)( 48,156)
( 49,193)( 50,194)( 51,199)( 52,200)( 53,198)( 54,197)( 55,195)( 56,196)
( 57,209)( 58,210)( 59,215)( 60,216)( 61,214)( 62,213)( 63,211)( 64,212)
( 65,201)( 66,202)( 67,207)( 68,208)( 69,206)( 70,205)( 71,203)( 72,204)
( 73,241)( 74,242)( 75,247)( 76,248)( 77,246)( 78,245)( 79,243)( 80,244)
( 81,257)( 82,258)( 83,263)( 84,264)( 85,262)( 86,261)( 87,259)( 88,260)
( 89,249)( 90,250)( 91,255)( 92,256)( 93,254)( 94,253)( 95,251)( 96,252)
( 97,217)( 98,218)( 99,223)(100,224)(101,222)(102,221)(103,219)(104,220)
(105,233)(106,234)(107,239)(108,240)(109,238)(110,237)(111,235)(112,236)
(113,225)(114,226)(115,231)(116,232)(117,230)(118,229)(119,227)(120,228)
(121,265)(122,266)(123,271)(124,272)(125,270)(126,269)(127,267)(128,268)
(129,281)(130,282)(131,287)(132,288)(133,286)(134,285)(135,283)(136,284)
(137,273)(138,274)(139,279)(140,280)(141,278)(142,277)(143,275)(144,276);;
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*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(288)!(  1,149)(  2,150)(  3,152)(  4,151)(  5,146)(  6,145)(  7,147)
(  8,148)(  9,165)( 10,166)( 11,168)( 12,167)( 13,162)( 14,161)( 15,163)
( 16,164)( 17,157)( 18,158)( 19,160)( 20,159)( 21,154)( 22,153)( 23,155)
( 24,156)( 25,173)( 26,174)( 27,176)( 28,175)( 29,170)( 30,169)( 31,171)
( 32,172)( 33,189)( 34,190)( 35,192)( 36,191)( 37,186)( 38,185)( 39,187)
( 40,188)( 41,181)( 42,182)( 43,184)( 44,183)( 45,178)( 46,177)( 47,179)
( 48,180)( 49,197)( 50,198)( 51,200)( 52,199)( 53,194)( 54,193)( 55,195)
( 56,196)( 57,213)( 58,214)( 59,216)( 60,215)( 61,210)( 62,209)( 63,211)
( 64,212)( 65,205)( 66,206)( 67,208)( 68,207)( 69,202)( 70,201)( 71,203)
( 72,204)( 73,221)( 74,222)( 75,224)( 76,223)( 77,218)( 78,217)( 79,219)
( 80,220)( 81,237)( 82,238)( 83,240)( 84,239)( 85,234)( 86,233)( 87,235)
( 88,236)( 89,229)( 90,230)( 91,232)( 92,231)( 93,226)( 94,225)( 95,227)
( 96,228)( 97,245)( 98,246)( 99,248)(100,247)(101,242)(102,241)(103,243)
(104,244)(105,261)(106,262)(107,264)(108,263)(109,258)(110,257)(111,259)
(112,260)(113,253)(114,254)(115,256)(116,255)(117,250)(118,249)(119,251)
(120,252)(121,269)(122,270)(123,272)(124,271)(125,266)(126,265)(127,267)
(128,268)(129,285)(130,286)(131,288)(132,287)(133,282)(134,281)(135,283)
(136,284)(137,277)(138,278)(139,280)(140,279)(141,274)(142,273)(143,275)
(144,276);
s1 := Sym(288)!(  1,  9)(  2, 10)(  3, 12)(  4, 11)(  5, 15)(  6, 16)(  7, 13)
(  8, 14)( 19, 20)( 21, 23)( 22, 24)( 25, 57)( 26, 58)( 27, 60)( 28, 59)
( 29, 63)( 30, 64)( 31, 61)( 32, 62)( 33, 49)( 34, 50)( 35, 52)( 36, 51)
( 37, 55)( 38, 56)( 39, 53)( 40, 54)( 41, 65)( 42, 66)( 43, 68)( 44, 67)
( 45, 71)( 46, 72)( 47, 69)( 48, 70)( 73, 81)( 74, 82)( 75, 84)( 76, 83)
( 77, 87)( 78, 88)( 79, 85)( 80, 86)( 91, 92)( 93, 95)( 94, 96)( 97,129)
( 98,130)( 99,132)(100,131)(101,135)(102,136)(103,133)(104,134)(105,121)
(106,122)(107,124)(108,123)(109,127)(110,128)(111,125)(112,126)(113,137)
(114,138)(115,140)(116,139)(117,143)(118,144)(119,141)(120,142)(145,226)
(146,225)(147,227)(148,228)(149,232)(150,231)(151,230)(152,229)(153,218)
(154,217)(155,219)(156,220)(157,224)(158,223)(159,222)(160,221)(161,234)
(162,233)(163,235)(164,236)(165,240)(166,239)(167,238)(168,237)(169,274)
(170,273)(171,275)(172,276)(173,280)(174,279)(175,278)(176,277)(177,266)
(178,265)(179,267)(180,268)(181,272)(182,271)(183,270)(184,269)(185,282)
(186,281)(187,283)(188,284)(189,288)(190,287)(191,286)(192,285)(193,250)
(194,249)(195,251)(196,252)(197,256)(198,255)(199,254)(200,253)(201,242)
(202,241)(203,243)(204,244)(205,248)(206,247)(207,246)(208,245)(209,258)
(210,257)(211,259)(212,260)(213,264)(214,263)(215,262)(216,261);
s2 := Sym(288)!(  1,169)(  2,170)(  3,175)(  4,176)(  5,174)(  6,173)(  7,171)
(  8,172)(  9,185)( 10,186)( 11,191)( 12,192)( 13,190)( 14,189)( 15,187)
( 16,188)( 17,177)( 18,178)( 19,183)( 20,184)( 21,182)( 22,181)( 23,179)
( 24,180)( 25,145)( 26,146)( 27,151)( 28,152)( 29,150)( 30,149)( 31,147)
( 32,148)( 33,161)( 34,162)( 35,167)( 36,168)( 37,166)( 38,165)( 39,163)
( 40,164)( 41,153)( 42,154)( 43,159)( 44,160)( 45,158)( 46,157)( 47,155)
( 48,156)( 49,193)( 50,194)( 51,199)( 52,200)( 53,198)( 54,197)( 55,195)
( 56,196)( 57,209)( 58,210)( 59,215)( 60,216)( 61,214)( 62,213)( 63,211)
( 64,212)( 65,201)( 66,202)( 67,207)( 68,208)( 69,206)( 70,205)( 71,203)
( 72,204)( 73,241)( 74,242)( 75,247)( 76,248)( 77,246)( 78,245)( 79,243)
( 80,244)( 81,257)( 82,258)( 83,263)( 84,264)( 85,262)( 86,261)( 87,259)
( 88,260)( 89,249)( 90,250)( 91,255)( 92,256)( 93,254)( 94,253)( 95,251)
( 96,252)( 97,217)( 98,218)( 99,223)(100,224)(101,222)(102,221)(103,219)
(104,220)(105,233)(106,234)(107,239)(108,240)(109,238)(110,237)(111,235)
(112,236)(113,225)(114,226)(115,231)(116,232)(117,230)(118,229)(119,227)
(120,228)(121,265)(122,266)(123,271)(124,272)(125,270)(126,269)(127,267)
(128,268)(129,281)(130,282)(131,287)(132,288)(133,286)(134,285)(135,283)
(136,284)(137,273)(138,274)(139,279)(140,280)(141,278)(142,277)(143,275)
(144,276);
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*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope