Polytope of Type {22,26}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,26}*1144
Also Known As : {22,26|2}. if this polytope has another name.
Group : SmallGroup(1144,35)
Rank : 3
Schlafli Type : {22,26}
Number of vertices, edges, etc : 22, 286, 26
Order of s₀s₁s₂ : 286
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) :
   11-fold quotients : {2,26}*104
   13-fold quotients : {22,2}*88
   22-fold quotients : {2,13}*52
   26-fold quotients : {11,2}*44
   143-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope