Polytope of Type {26,22}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope