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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}*1152s
if this polytope has a name.
Group : SmallGroup(1152,155849)
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}*576i
   3-fold quotients : {4,24}*384f
   4-fold quotients : {12,6}*288b
   6-fold quotients : {4,12}*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)
( 73,222)( 74,221)( 75,223)( 76,224)( 77,217)( 78,218)( 79,220)( 80,219)
( 81,238)( 82,237)( 83,239)( 84,240)( 85,233)( 86,234)( 87,236)( 88,235)
( 89,230)( 90,229)( 91,231)( 92,232)( 93,225)( 94,226)( 95,228)( 96,227)
( 97,246)( 98,245)( 99,247)(100,248)(101,241)(102,242)(103,244)(104,243)
(105,262)(106,261)(107,263)(108,264)(109,257)(110,258)(111,260)(112,259)
(113,254)(114,253)(115,255)(116,256)(117,249)(118,250)(119,252)(120,251)
(121,270)(122,269)(123,271)(124,272)(125,265)(126,266)(127,268)(128,267)
(129,286)(130,285)(131,287)(132,288)(133,281)(134,282)(135,284)(136,283)
(137,278)(138,277)(139,279)(140,280)(141,273)(142,274)(143,276)(144,275);;
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, 82)( 74, 81)( 75, 83)( 76, 84)( 77, 88)
( 78, 87)( 79, 86)( 80, 85)( 89, 90)( 93, 96)( 94, 95)( 97,130)( 98,129)
( 99,131)(100,132)(101,136)(102,135)(103,134)(104,133)(105,122)(106,121)
(107,123)(108,124)(109,128)(110,127)(111,126)(112,125)(113,138)(114,137)
(115,139)(116,140)(117,144)(118,143)(119,142)(120,141)(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)
( 73,242)( 74,241)( 75,248)( 76,247)( 77,245)( 78,246)( 79,244)( 80,243)
( 81,258)( 82,257)( 83,264)( 84,263)( 85,261)( 86,262)( 87,260)( 88,259)
( 89,250)( 90,249)( 91,256)( 92,255)( 93,253)( 94,254)( 95,252)( 96,251)
( 97,218)( 98,217)( 99,224)(100,223)(101,221)(102,222)(103,220)(104,219)
(105,234)(106,233)(107,240)(108,239)(109,237)(110,238)(111,236)(112,235)
(113,226)(114,225)(115,232)(116,231)(117,229)(118,230)(119,228)(120,227)
(121,266)(122,265)(123,272)(124,271)(125,269)(126,270)(127,268)(128,267)
(129,282)(130,281)(131,288)(132,287)(133,285)(134,286)(135,284)(136,283)
(137,274)(138,273)(139,280)(140,279)(141,277)(142,278)(143,276)(144,275);;
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*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)!(  1,149)(  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)( 73,222)( 74,221)( 75,223)( 76,224)( 77,217)( 78,218)( 79,220)
( 80,219)( 81,238)( 82,237)( 83,239)( 84,240)( 85,233)( 86,234)( 87,236)
( 88,235)( 89,230)( 90,229)( 91,231)( 92,232)( 93,225)( 94,226)( 95,228)
( 96,227)( 97,246)( 98,245)( 99,247)(100,248)(101,241)(102,242)(103,244)
(104,243)(105,262)(106,261)(107,263)(108,264)(109,257)(110,258)(111,260)
(112,259)(113,254)(114,253)(115,255)(116,256)(117,249)(118,250)(119,252)
(120,251)(121,270)(122,269)(123,271)(124,272)(125,265)(126,266)(127,268)
(128,267)(129,286)(130,285)(131,287)(132,288)(133,281)(134,282)(135,284)
(136,283)(137,278)(138,277)(139,279)(140,280)(141,273)(142,274)(143,276)
(144,275);
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, 82)( 74, 81)( 75, 83)( 76, 84)
( 77, 88)( 78, 87)( 79, 86)( 80, 85)( 89, 90)( 93, 96)( 94, 95)( 97,130)
( 98,129)( 99,131)(100,132)(101,136)(102,135)(103,134)(104,133)(105,122)
(106,121)(107,123)(108,124)(109,128)(110,127)(111,126)(112,125)(113,138)
(114,137)(115,139)(116,140)(117,144)(118,143)(119,142)(120,141)(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)( 73,242)( 74,241)( 75,248)( 76,247)( 77,245)( 78,246)( 79,244)
( 80,243)( 81,258)( 82,257)( 83,264)( 84,263)( 85,261)( 86,262)( 87,260)
( 88,259)( 89,250)( 90,249)( 91,256)( 92,255)( 93,253)( 94,254)( 95,252)
( 96,251)( 97,218)( 98,217)( 99,224)(100,223)(101,221)(102,222)(103,220)
(104,219)(105,234)(106,233)(107,240)(108,239)(109,237)(110,238)(111,236)
(112,235)(113,226)(114,225)(115,232)(116,231)(117,229)(118,230)(119,228)
(120,227)(121,266)(122,265)(123,272)(124,271)(125,269)(126,270)(127,268)
(128,267)(129,282)(130,281)(131,288)(132,287)(133,285)(134,286)(135,284)
(136,283)(137,274)(138,273)(139,280)(140,279)(141,277)(142,278)(143,276)
(144,275);
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*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