Polytope of Type {6,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,24}*1152h
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 : 4
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}*576b
   3-fold quotients : {6,8}*384g
   4-fold quotients : {6,24}*288a, {6,12}*288a
   6-fold quotients : {6,4}*192b
   8-fold quotients : {6,12}*144a, {6,12}*144d
   12-fold quotients : {2,24}*96, {6,8}*96, {6,4}*96
   16-fold quotients : {6,6}*72a
   24-fold quotients : {2,12}*48, {6,4}*48a, {3,4}*48, {6,4}*48b, {6,4}*48c
   36-fold quotients : {2,8}*32
   48-fold quotients : {3,4}*24, {2,6}*24, {6,2}*24
   72-fold quotients : {2,4}*16
   96-fold quotients : {2,3}*12, {3,2}*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)(  3,152)(  4,151)(  5,146)(  6,145)(  7,148)(  8,147)
(  9,154)( 10,153)( 11,156)( 12,155)( 13,162)( 14,161)( 15,164)( 16,163)
( 17,158)( 18,157)( 19,160)( 20,159)( 21,166)( 22,165)( 23,168)( 24,167)
( 25,174)( 26,173)( 27,176)( 28,175)( 29,170)( 30,169)( 31,172)( 32,171)
( 33,178)( 34,177)( 35,180)( 36,179)( 37,186)( 38,185)( 39,188)( 40,187)
( 41,182)( 42,181)( 43,184)( 44,183)( 45,190)( 46,189)( 47,192)( 48,191)
( 49,198)( 50,197)( 51,200)( 52,199)( 53,194)( 54,193)( 55,196)( 56,195)
( 57,202)( 58,201)( 59,204)( 60,203)( 61,210)( 62,209)( 63,212)( 64,211)
( 65,206)( 66,205)( 67,208)( 68,207)( 69,214)( 70,213)( 71,216)( 72,215)
( 73,258)( 74,257)( 75,260)( 76,259)( 77,254)( 78,253)( 79,256)( 80,255)
( 81,262)( 82,261)( 83,264)( 84,263)( 85,270)( 86,269)( 87,272)( 88,271)
( 89,266)( 90,265)( 91,268)( 92,267)( 93,274)( 94,273)( 95,276)( 96,275)
( 97,282)( 98,281)( 99,284)(100,283)(101,278)(102,277)(103,280)(104,279)
(105,286)(106,285)(107,288)(108,287)(109,222)(110,221)(111,224)(112,223)
(113,218)(114,217)(115,220)(116,219)(117,226)(118,225)(119,228)(120,227)
(121,234)(122,233)(123,236)(124,235)(125,230)(126,229)(127,232)(128,231)
(129,238)(130,237)(131,240)(132,239)(133,246)(134,245)(135,248)(136,247)
(137,242)(138,241)(139,244)(140,243)(141,250)(142,249)(143,252)(144,251);;
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, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*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)(  3,152)(  4,151)(  5,146)(  6,145)(  7,148)
(  8,147)(  9,154)( 10,153)( 11,156)( 12,155)( 13,162)( 14,161)( 15,164)
( 16,163)( 17,158)( 18,157)( 19,160)( 20,159)( 21,166)( 22,165)( 23,168)
( 24,167)( 25,174)( 26,173)( 27,176)( 28,175)( 29,170)( 30,169)( 31,172)
( 32,171)( 33,178)( 34,177)( 35,180)( 36,179)( 37,186)( 38,185)( 39,188)
( 40,187)( 41,182)( 42,181)( 43,184)( 44,183)( 45,190)( 46,189)( 47,192)
( 48,191)( 49,198)( 50,197)( 51,200)( 52,199)( 53,194)( 54,193)( 55,196)
( 56,195)( 57,202)( 58,201)( 59,204)( 60,203)( 61,210)( 62,209)( 63,212)
( 64,211)( 65,206)( 66,205)( 67,208)( 68,207)( 69,214)( 70,213)( 71,216)
( 72,215)( 73,258)( 74,257)( 75,260)( 76,259)( 77,254)( 78,253)( 79,256)
( 80,255)( 81,262)( 82,261)( 83,264)( 84,263)( 85,270)( 86,269)( 87,272)
( 88,271)( 89,266)( 90,265)( 91,268)( 92,267)( 93,274)( 94,273)( 95,276)
( 96,275)( 97,282)( 98,281)( 99,284)(100,283)(101,278)(102,277)(103,280)
(104,279)(105,286)(106,285)(107,288)(108,287)(109,222)(110,221)(111,224)
(112,223)(113,218)(114,217)(115,220)(116,219)(117,226)(118,225)(119,228)
(120,227)(121,234)(122,233)(123,236)(124,235)(125,230)(126,229)(127,232)
(128,231)(129,238)(130,237)(131,240)(132,239)(133,246)(134,245)(135,248)
(136,247)(137,242)(138,241)(139,244)(140,243)(141,250)(142,249)(143,252)
(144,251);
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, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*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