Polytope of Type {6,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,24}*1152g
if this polytope has a name.
Group : SmallGroup(1152,155812)
Rank : 3
Schlafli Type : {6,24}
Number of vertices, edges, etc : 24, 288, 96
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,12}*576a
   3-fold quotients : {6,24}*384a
   4-fold quotients : {6,24}*288b, {6,6}*288a
   6-fold quotients : {6,12}*192a
   8-fold quotients : {6,12}*144b, {6,3}*144
   12-fold quotients : {2,24}*96, {6,6}*96
   16-fold quotients : {6,6}*72b
   24-fold quotients : {2,12}*48, {3,6}*48, {6,3}*48
   32-fold quotients : {6,3}*36
   36-fold quotients : {2,8}*32
   48-fold quotients : {3,3}*24, {2,6}*24
   72-fold quotients : {2,4}*16
   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 := (  3,  4)(  7,  8)( 11, 12)( 13, 25)( 14, 26)( 15, 28)( 16, 27)( 17, 29)
( 18, 30)( 19, 32)( 20, 31)( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 39, 40)
( 43, 44)( 47, 48)( 49, 61)( 50, 62)( 51, 64)( 52, 63)( 53, 65)( 54, 66)
( 55, 68)( 56, 67)( 57, 69)( 58, 70)( 59, 72)( 60, 71)( 75, 76)( 79, 80)
( 83, 84)( 85, 97)( 86, 98)( 87,100)( 88, 99)( 89,101)( 90,102)( 91,104)
( 92,103)( 93,105)( 94,106)( 95,108)( 96,107)(111,112)(115,116)(119,120)
(121,133)(122,134)(123,136)(124,135)(125,137)(126,138)(127,140)(128,139)
(129,141)(130,142)(131,144)(132,143)(147,148)(151,152)(155,156)(157,169)
(158,170)(159,172)(160,171)(161,173)(162,174)(163,176)(164,175)(165,177)
(166,178)(167,180)(168,179)(183,184)(187,188)(191,192)(193,205)(194,206)
(195,208)(196,207)(197,209)(198,210)(199,212)(200,211)(201,213)(202,214)
(203,216)(204,215)(219,220)(223,224)(227,228)(229,241)(230,242)(231,244)
(232,243)(233,245)(234,246)(235,248)(236,247)(237,249)(238,250)(239,252)
(240,251)(255,256)(259,260)(263,264)(265,277)(266,278)(267,280)(268,279)
(269,281)(270,282)(271,284)(272,283)(273,285)(274,286)(275,288)(276,287);;
s1 := (  1, 13)(  2, 16)(  3, 15)(  4, 14)(  5, 21)(  6, 24)(  7, 23)(  8, 22)
(  9, 17)( 10, 20)( 11, 19)( 12, 18)( 26, 28)( 29, 33)( 30, 36)( 31, 35)
( 32, 34)( 37, 49)( 38, 52)( 39, 51)( 40, 50)( 41, 57)( 42, 60)( 43, 59)
( 44, 58)( 45, 53)( 46, 56)( 47, 55)( 48, 54)( 62, 64)( 65, 69)( 66, 72)
( 67, 71)( 68, 70)( 73,121)( 74,124)( 75,123)( 76,122)( 77,129)( 78,132)
( 79,131)( 80,130)( 81,125)( 82,128)( 83,127)( 84,126)( 85,109)( 86,112)
( 87,111)( 88,110)( 89,117)( 90,120)( 91,119)( 92,118)( 93,113)( 94,116)
( 95,115)( 96,114)( 97,133)( 98,136)( 99,135)(100,134)(101,141)(102,144)
(103,143)(104,142)(105,137)(106,140)(107,139)(108,138)(145,229)(146,232)
(147,231)(148,230)(149,237)(150,240)(151,239)(152,238)(153,233)(154,236)
(155,235)(156,234)(157,217)(158,220)(159,219)(160,218)(161,225)(162,228)
(163,227)(164,226)(165,221)(166,224)(167,223)(168,222)(169,241)(170,244)
(171,243)(172,242)(173,249)(174,252)(175,251)(176,250)(177,245)(178,248)
(179,247)(180,246)(181,265)(182,268)(183,267)(184,266)(185,273)(186,276)
(187,275)(188,274)(189,269)(190,272)(191,271)(192,270)(193,253)(194,256)
(195,255)(196,254)(197,261)(198,264)(199,263)(200,262)(201,257)(202,260)
(203,259)(204,258)(205,277)(206,280)(207,279)(208,278)(209,285)(210,288)
(211,287)(212,286)(213,281)(214,284)(215,283)(216,282);;
s2 := (  1,150)(  2,149)(  3,151)(  4,152)(  5,146)(  6,145)(  7,147)(  8,148)
(  9,154)( 10,153)( 11,155)( 12,156)( 13,174)( 14,173)( 15,175)( 16,176)
( 17,170)( 18,169)( 19,171)( 20,172)( 21,178)( 22,177)( 23,179)( 24,180)
( 25,162)( 26,161)( 27,163)( 28,164)( 29,158)( 30,157)( 31,159)( 32,160)
( 33,166)( 34,165)( 35,167)( 36,168)( 37,186)( 38,185)( 39,187)( 40,188)
( 41,182)( 42,181)( 43,183)( 44,184)( 45,190)( 46,189)( 47,191)( 48,192)
( 49,210)( 50,209)( 51,211)( 52,212)( 53,206)( 54,205)( 55,207)( 56,208)
( 57,214)( 58,213)( 59,215)( 60,216)( 61,198)( 62,197)( 63,199)( 64,200)
( 65,194)( 66,193)( 67,195)( 68,196)( 69,202)( 70,201)( 71,203)( 72,204)
( 73,258)( 74,257)( 75,259)( 76,260)( 77,254)( 78,253)( 79,255)( 80,256)
( 81,262)( 82,261)( 83,263)( 84,264)( 85,282)( 86,281)( 87,283)( 88,284)
( 89,278)( 90,277)( 91,279)( 92,280)( 93,286)( 94,285)( 95,287)( 96,288)
( 97,270)( 98,269)( 99,271)(100,272)(101,266)(102,265)(103,267)(104,268)
(105,274)(106,273)(107,275)(108,276)(109,222)(110,221)(111,223)(112,224)
(113,218)(114,217)(115,219)(116,220)(117,226)(118,225)(119,227)(120,228)
(121,246)(122,245)(123,247)(124,248)(125,242)(126,241)(127,243)(128,244)
(129,250)(130,249)(131,251)(132,252)(133,234)(134,233)(135,235)(136,236)
(137,230)(138,229)(139,231)(140,232)(141,238)(142,237)(143,239)(144,240);;
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, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(288)!(  3,  4)(  7,  8)( 11, 12)( 13, 25)( 14, 26)( 15, 28)( 16, 27)
( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 33)( 22, 34)( 23, 36)( 24, 35)
( 39, 40)( 43, 44)( 47, 48)( 49, 61)( 50, 62)( 51, 64)( 52, 63)( 53, 65)
( 54, 66)( 55, 68)( 56, 67)( 57, 69)( 58, 70)( 59, 72)( 60, 71)( 75, 76)
( 79, 80)( 83, 84)( 85, 97)( 86, 98)( 87,100)( 88, 99)( 89,101)( 90,102)
( 91,104)( 92,103)( 93,105)( 94,106)( 95,108)( 96,107)(111,112)(115,116)
(119,120)(121,133)(122,134)(123,136)(124,135)(125,137)(126,138)(127,140)
(128,139)(129,141)(130,142)(131,144)(132,143)(147,148)(151,152)(155,156)
(157,169)(158,170)(159,172)(160,171)(161,173)(162,174)(163,176)(164,175)
(165,177)(166,178)(167,180)(168,179)(183,184)(187,188)(191,192)(193,205)
(194,206)(195,208)(196,207)(197,209)(198,210)(199,212)(200,211)(201,213)
(202,214)(203,216)(204,215)(219,220)(223,224)(227,228)(229,241)(230,242)
(231,244)(232,243)(233,245)(234,246)(235,248)(236,247)(237,249)(238,250)
(239,252)(240,251)(255,256)(259,260)(263,264)(265,277)(266,278)(267,280)
(268,279)(269,281)(270,282)(271,284)(272,283)(273,285)(274,286)(275,288)
(276,287);
s1 := Sym(288)!(  1, 13)(  2, 16)(  3, 15)(  4, 14)(  5, 21)(  6, 24)(  7, 23)
(  8, 22)(  9, 17)( 10, 20)( 11, 19)( 12, 18)( 26, 28)( 29, 33)( 30, 36)
( 31, 35)( 32, 34)( 37, 49)( 38, 52)( 39, 51)( 40, 50)( 41, 57)( 42, 60)
( 43, 59)( 44, 58)( 45, 53)( 46, 56)( 47, 55)( 48, 54)( 62, 64)( 65, 69)
( 66, 72)( 67, 71)( 68, 70)( 73,121)( 74,124)( 75,123)( 76,122)( 77,129)
( 78,132)( 79,131)( 80,130)( 81,125)( 82,128)( 83,127)( 84,126)( 85,109)
( 86,112)( 87,111)( 88,110)( 89,117)( 90,120)( 91,119)( 92,118)( 93,113)
( 94,116)( 95,115)( 96,114)( 97,133)( 98,136)( 99,135)(100,134)(101,141)
(102,144)(103,143)(104,142)(105,137)(106,140)(107,139)(108,138)(145,229)
(146,232)(147,231)(148,230)(149,237)(150,240)(151,239)(152,238)(153,233)
(154,236)(155,235)(156,234)(157,217)(158,220)(159,219)(160,218)(161,225)
(162,228)(163,227)(164,226)(165,221)(166,224)(167,223)(168,222)(169,241)
(170,244)(171,243)(172,242)(173,249)(174,252)(175,251)(176,250)(177,245)
(178,248)(179,247)(180,246)(181,265)(182,268)(183,267)(184,266)(185,273)
(186,276)(187,275)(188,274)(189,269)(190,272)(191,271)(192,270)(193,253)
(194,256)(195,255)(196,254)(197,261)(198,264)(199,263)(200,262)(201,257)
(202,260)(203,259)(204,258)(205,277)(206,280)(207,279)(208,278)(209,285)
(210,288)(211,287)(212,286)(213,281)(214,284)(215,283)(216,282);
s2 := Sym(288)!(  1,150)(  2,149)(  3,151)(  4,152)(  5,146)(  6,145)(  7,147)
(  8,148)(  9,154)( 10,153)( 11,155)( 12,156)( 13,174)( 14,173)( 15,175)
( 16,176)( 17,170)( 18,169)( 19,171)( 20,172)( 21,178)( 22,177)( 23,179)
( 24,180)( 25,162)( 26,161)( 27,163)( 28,164)( 29,158)( 30,157)( 31,159)
( 32,160)( 33,166)( 34,165)( 35,167)( 36,168)( 37,186)( 38,185)( 39,187)
( 40,188)( 41,182)( 42,181)( 43,183)( 44,184)( 45,190)( 46,189)( 47,191)
( 48,192)( 49,210)( 50,209)( 51,211)( 52,212)( 53,206)( 54,205)( 55,207)
( 56,208)( 57,214)( 58,213)( 59,215)( 60,216)( 61,198)( 62,197)( 63,199)
( 64,200)( 65,194)( 66,193)( 67,195)( 68,196)( 69,202)( 70,201)( 71,203)
( 72,204)( 73,258)( 74,257)( 75,259)( 76,260)( 77,254)( 78,253)( 79,255)
( 80,256)( 81,262)( 82,261)( 83,263)( 84,264)( 85,282)( 86,281)( 87,283)
( 88,284)( 89,278)( 90,277)( 91,279)( 92,280)( 93,286)( 94,285)( 95,287)
( 96,288)( 97,270)( 98,269)( 99,271)(100,272)(101,266)(102,265)(103,267)
(104,268)(105,274)(106,273)(107,275)(108,276)(109,222)(110,221)(111,223)
(112,224)(113,218)(114,217)(115,219)(116,220)(117,226)(118,225)(119,227)
(120,228)(121,246)(122,245)(123,247)(124,248)(125,242)(126,241)(127,243)
(128,244)(129,250)(130,249)(131,251)(132,252)(133,234)(134,233)(135,235)
(136,236)(137,230)(138,229)(139,231)(140,232)(141,238)(142,237)(143,239)
(144,240);
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, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope