Polytope of Type {6,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,24}*1152b
if this polytope has a name.
Group : SmallGroup(1152,155485)
Rank : 3
Schlafli Type : {6,24}
Number of vertices, edges, etc : 24, 288, 96
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 : {3,24}*576
   3-fold quotients : {6,8}*384e
   4-fold quotients : {6,12}*288b
   6-fold quotients : {3,8}*192
   8-fold quotients : {3,12}*144
   12-fold quotients : {6,4}*96
   16-fold quotients : {6,6}*72c
   24-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
   32-fold quotients : {3,6}*36
   48-fold quotients : {3,4}*24, {6,2}*24
   96-fold quotients : {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)(  9, 16)( 10, 15)( 11, 13)( 12, 14)( 17, 33)( 18, 34)
( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 48)( 26, 47)
( 27, 45)( 28, 46)( 29, 43)( 30, 44)( 31, 42)( 32, 41)( 49, 97)( 50, 98)
( 51,100)( 52, 99)( 53,101)( 54,102)( 55,104)( 56,103)( 57,112)( 58,111)
( 59,109)( 60,110)( 61,107)( 62,108)( 63,106)( 64,105)( 65,129)( 66,130)
( 67,132)( 68,131)( 69,133)( 70,134)( 71,136)( 72,135)( 73,144)( 74,143)
( 75,141)( 76,142)( 77,139)( 78,140)( 79,138)( 80,137)( 81,113)( 82,114)
( 83,116)( 84,115)( 85,117)( 86,118)( 87,120)( 88,119)( 89,128)( 90,127)
( 91,125)( 92,126)( 93,123)( 94,124)( 95,122)( 96,121)(147,148)(151,152)
(153,160)(154,159)(155,157)(156,158)(161,177)(162,178)(163,180)(164,179)
(165,181)(166,182)(167,184)(168,183)(169,192)(170,191)(171,189)(172,190)
(173,187)(174,188)(175,186)(176,185)(193,241)(194,242)(195,244)(196,243)
(197,245)(198,246)(199,248)(200,247)(201,256)(202,255)(203,253)(204,254)
(205,251)(206,252)(207,250)(208,249)(209,273)(210,274)(211,276)(212,275)
(213,277)(214,278)(215,280)(216,279)(217,288)(218,287)(219,285)(220,286)
(221,283)(222,284)(223,282)(224,281)(225,257)(226,258)(227,260)(228,259)
(229,261)(230,262)(231,264)(232,263)(233,272)(234,271)(235,269)(236,270)
(237,267)(238,268)(239,266)(240,265);;
s1 := (  1,209)(  2,212)(  3,211)(  4,210)(  5,223)(  6,222)(  7,221)(  8,224)
(  9,219)( 10,218)( 11,217)( 12,220)( 13,215)( 14,214)( 15,213)( 16,216)
( 17,193)( 18,196)( 19,195)( 20,194)( 21,207)( 22,206)( 23,205)( 24,208)
( 25,203)( 26,202)( 27,201)( 28,204)( 29,199)( 30,198)( 31,197)( 32,200)
( 33,225)( 34,228)( 35,227)( 36,226)( 37,239)( 38,238)( 39,237)( 40,240)
( 41,235)( 42,234)( 43,233)( 44,236)( 45,231)( 46,230)( 47,229)( 48,232)
( 49,161)( 50,164)( 51,163)( 52,162)( 53,175)( 54,174)( 55,173)( 56,176)
( 57,171)( 58,170)( 59,169)( 60,172)( 61,167)( 62,166)( 63,165)( 64,168)
( 65,145)( 66,148)( 67,147)( 68,146)( 69,159)( 70,158)( 71,157)( 72,160)
( 73,155)( 74,154)( 75,153)( 76,156)( 77,151)( 78,150)( 79,149)( 80,152)
( 81,177)( 82,180)( 83,179)( 84,178)( 85,191)( 86,190)( 87,189)( 88,192)
( 89,187)( 90,186)( 91,185)( 92,188)( 93,183)( 94,182)( 95,181)( 96,184)
( 97,257)( 98,260)( 99,259)(100,258)(101,271)(102,270)(103,269)(104,272)
(105,267)(106,266)(107,265)(108,268)(109,263)(110,262)(111,261)(112,264)
(113,241)(114,244)(115,243)(116,242)(117,255)(118,254)(119,253)(120,256)
(121,251)(122,250)(123,249)(124,252)(125,247)(126,246)(127,245)(128,248)
(129,273)(130,276)(131,275)(132,274)(133,287)(134,286)(135,285)(136,288)
(137,283)(138,282)(139,281)(140,284)(141,279)(142,278)(143,277)(144,280);;
s2 := (  1,  5)(  2,  6)(  3,  7)(  4,  8)(  9, 15)( 10, 16)( 11, 13)( 12, 14)
( 17, 37)( 18, 38)( 19, 39)( 20, 40)( 21, 33)( 22, 34)( 23, 35)( 24, 36)
( 25, 47)( 26, 48)( 27, 45)( 28, 46)( 29, 43)( 30, 44)( 31, 41)( 32, 42)
( 49, 53)( 50, 54)( 51, 55)( 52, 56)( 57, 63)( 58, 64)( 59, 61)( 60, 62)
( 65, 85)( 66, 86)( 67, 87)( 68, 88)( 69, 81)( 70, 82)( 71, 83)( 72, 84)
( 73, 95)( 74, 96)( 75, 93)( 76, 94)( 77, 91)( 78, 92)( 79, 89)( 80, 90)
( 97,101)( 98,102)( 99,103)(100,104)(105,111)(106,112)(107,109)(108,110)
(113,133)(114,134)(115,135)(116,136)(117,129)(118,130)(119,131)(120,132)
(121,143)(122,144)(123,141)(124,142)(125,139)(126,140)(127,137)(128,138)
(145,149)(146,150)(147,151)(148,152)(153,159)(154,160)(155,157)(156,158)
(161,181)(162,182)(163,183)(164,184)(165,177)(166,178)(167,179)(168,180)
(169,191)(170,192)(171,189)(172,190)(173,187)(174,188)(175,185)(176,186)
(193,197)(194,198)(195,199)(196,200)(201,207)(202,208)(203,205)(204,206)
(209,229)(210,230)(211,231)(212,232)(213,225)(214,226)(215,227)(216,228)
(217,239)(218,240)(219,237)(220,238)(221,235)(222,236)(223,233)(224,234)
(241,245)(242,246)(243,247)(244,248)(249,255)(250,256)(251,253)(252,254)
(257,277)(258,278)(259,279)(260,280)(261,273)(262,274)(263,275)(264,276)
(265,287)(266,288)(267,285)(268,286)(269,283)(270,284)(271,281)(272,282);;
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*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope