Polytope of Type {24,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,6}*1152k
if this polytope has a name.
Group : SmallGroup(1152,156074)
Rank : 3
Schlafli Type : {24,6}
Number of vertices, edges, etc : 96, 288, 24
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 12
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 : {12,6}*576f
   3-fold quotients : {8,6}*384g
   4-fold quotients : {24,6}*288c, {12,6}*288b
   6-fold quotients : {4,6}*192b
   8-fold quotients : {12,6}*144c, {12,3}*144
   12-fold quotients : {8,6}*96, {4,6}*96
   16-fold quotients : {6,6}*72b
   24-fold quotients : {4,6}*48a, {4,3}*48, {4,6}*48b, {4,6}*48c
   32-fold quotients : {6,3}*36
   36-fold quotients : {8,2}*32
   48-fold quotients : {4,3}*24, {2,6}*24
   72-fold quotients : {4,2}*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 := (  1,  3)(  2,  4)(  5, 11)(  6, 12)(  7,  9)(  8, 10)( 13, 15)( 14, 16)
( 17, 23)( 18, 24)( 19, 21)( 20, 22)( 25, 27)( 26, 28)( 29, 35)( 30, 36)
( 31, 33)( 32, 34)( 37, 39)( 38, 40)( 41, 47)( 42, 48)( 43, 45)( 44, 46)
( 49, 51)( 50, 52)( 53, 59)( 54, 60)( 55, 57)( 56, 58)( 61, 63)( 62, 64)
( 65, 71)( 66, 72)( 67, 69)( 68, 70)( 73,111)( 74,112)( 75,109)( 76,110)
( 77,119)( 78,120)( 79,117)( 80,118)( 81,115)( 82,116)( 83,113)( 84,114)
( 85,123)( 86,124)( 87,121)( 88,122)( 89,131)( 90,132)( 91,129)( 92,130)
( 93,127)( 94,128)( 95,125)( 96,126)( 97,135)( 98,136)( 99,133)(100,134)
(101,143)(102,144)(103,141)(104,142)(105,139)(106,140)(107,137)(108,138)
(145,219)(146,220)(147,217)(148,218)(149,227)(150,228)(151,225)(152,226)
(153,223)(154,224)(155,221)(156,222)(157,231)(158,232)(159,229)(160,230)
(161,239)(162,240)(163,237)(164,238)(165,235)(166,236)(167,233)(168,234)
(169,243)(170,244)(171,241)(172,242)(173,251)(174,252)(175,249)(176,250)
(177,247)(178,248)(179,245)(180,246)(181,255)(182,256)(183,253)(184,254)
(185,263)(186,264)(187,261)(188,262)(189,259)(190,260)(191,257)(192,258)
(193,267)(194,268)(195,265)(196,266)(197,275)(198,276)(199,273)(200,274)
(201,271)(202,272)(203,269)(204,270)(205,279)(206,280)(207,277)(208,278)
(209,287)(210,288)(211,285)(212,286)(213,283)(214,284)(215,281)(216,282);;
s1 := (  1,149)(  2,150)(  3,152)(  4,151)(  5,145)(  6,146)(  7,148)(  8,147)
(  9,153)( 10,154)( 11,156)( 12,155)( 13,173)( 14,174)( 15,176)( 16,175)
( 17,169)( 18,170)( 19,172)( 20,171)( 21,177)( 22,178)( 23,180)( 24,179)
( 25,161)( 26,162)( 27,164)( 28,163)( 29,157)( 30,158)( 31,160)( 32,159)
( 33,165)( 34,166)( 35,168)( 36,167)( 37,185)( 38,186)( 39,188)( 40,187)
( 41,181)( 42,182)( 43,184)( 44,183)( 45,189)( 46,190)( 47,192)( 48,191)
( 49,209)( 50,210)( 51,212)( 52,211)( 53,205)( 54,206)( 55,208)( 56,207)
( 57,213)( 58,214)( 59,216)( 60,215)( 61,197)( 62,198)( 63,200)( 64,199)
( 65,193)( 66,194)( 67,196)( 68,195)( 69,201)( 70,202)( 71,204)( 72,203)
( 73,257)( 74,258)( 75,260)( 76,259)( 77,253)( 78,254)( 79,256)( 80,255)
( 81,261)( 82,262)( 83,264)( 84,263)( 85,281)( 86,282)( 87,284)( 88,283)
( 89,277)( 90,278)( 91,280)( 92,279)( 93,285)( 94,286)( 95,288)( 96,287)
( 97,269)( 98,270)( 99,272)(100,271)(101,265)(102,266)(103,268)(104,267)
(105,273)(106,274)(107,276)(108,275)(109,221)(110,222)(111,224)(112,223)
(113,217)(114,218)(115,220)(116,219)(117,225)(118,226)(119,228)(120,227)
(121,245)(122,246)(123,248)(124,247)(125,241)(126,242)(127,244)(128,243)
(129,249)(130,250)(131,252)(132,251)(133,233)(134,234)(135,236)(136,235)
(137,229)(138,230)(139,232)(140,231)(141,237)(142,238)(143,240)(144,239);;
s2 := (  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, 85)( 74, 88)( 75, 87)( 76, 86)( 77, 93)( 78, 96)
( 79, 95)( 80, 94)( 81, 89)( 82, 92)( 83, 91)( 84, 90)( 98,100)(101,105)
(102,108)(103,107)(104,106)(109,121)(110,124)(111,123)(112,122)(113,129)
(114,132)(115,131)(116,130)(117,125)(118,128)(119,127)(120,126)(134,136)
(137,141)(138,144)(139,143)(140,142)(145,157)(146,160)(147,159)(148,158)
(149,165)(150,168)(151,167)(152,166)(153,161)(154,164)(155,163)(156,162)
(170,172)(173,177)(174,180)(175,179)(176,178)(181,193)(182,196)(183,195)
(184,194)(185,201)(186,204)(187,203)(188,202)(189,197)(190,200)(191,199)
(192,198)(206,208)(209,213)(210,216)(211,215)(212,214)(217,229)(218,232)
(219,231)(220,230)(221,237)(222,240)(223,239)(224,238)(225,233)(226,236)
(227,235)(228,234)(242,244)(245,249)(246,252)(247,251)(248,250)(253,265)
(254,268)(255,267)(256,266)(257,273)(258,276)(259,275)(260,274)(261,269)
(262,272)(263,271)(264,270)(278,280)(281,285)(282,288)(283,287)(284,286);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope