Polytope of Type {24,22}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,22}*1056
Also Known As : {24,22|2}. if this polytope has another name.
Group : SmallGroup(1056,235)
Rank : 3
Schlafli Type : {24,22}
Number of vertices, edges, etc : 24, 264, 22
Order of s₀s₁s₂ : 264
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
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 : {12,22}*528
   3-fold quotients : {8,22}*352
   4-fold quotients : {6,22}*264
   6-fold quotients : {4,22}*176
   11-fold quotients : {24,2}*96
   12-fold quotients : {2,22}*88
   22-fold quotients : {12,2}*48
   24-fold quotients : {2,11}*44
   33-fold quotients : {8,2}*32
   44-fold quotients : {6,2}*24
   66-fold quotients : {4,2}*16
   88-fold quotients : {3,2}*12
   132-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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