Polytope of Type {22,24}

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

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