Polytope of Type {26,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {26,20}*1040
Also Known As : {26,20|2}. if this polytope has another name.
Group : SmallGroup(1040,166)
Rank : 3
Schlafli Type : {26,20}
Number of vertices, edges, etc : 26, 260, 20
Order of s₀s₁s₂ : 260
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 : {26,10}*520
   5-fold quotients : {26,4}*208
   10-fold quotients : {26,2}*104
   13-fold quotients : {2,20}*80
   20-fold quotients : {13,2}*52
   26-fold quotients : {2,10}*40
   52-fold quotients : {2,5}*20
   65-fold quotients : {2,4}*16
   130-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);;
s1 := (  1,  2)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 14, 54)( 15, 53)
( 16, 65)( 17, 64)( 18, 63)( 19, 62)( 20, 61)( 21, 60)( 22, 59)( 23, 58)
( 24, 57)( 25, 56)( 26, 55)( 27, 41)( 28, 40)( 29, 52)( 30, 51)( 31, 50)
( 32, 49)( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 42)
( 66, 67)( 68, 78)( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 79,119)( 80,118)
( 81,130)( 82,129)( 83,128)( 84,127)( 85,126)( 86,125)( 87,124)( 88,123)
( 89,122)( 90,121)( 91,120)( 92,106)( 93,105)( 94,117)( 95,116)( 96,115)
( 97,114)( 98,113)( 99,112)(100,111)(101,110)(102,109)(103,108)(104,107)
(131,197)(132,196)(133,208)(134,207)(135,206)(136,205)(137,204)(138,203)
(139,202)(140,201)(141,200)(142,199)(143,198)(144,249)(145,248)(146,260)
(147,259)(148,258)(149,257)(150,256)(151,255)(152,254)(153,253)(154,252)
(155,251)(156,250)(157,236)(158,235)(159,247)(160,246)(161,245)(162,244)
(163,243)(164,242)(165,241)(166,240)(167,239)(168,238)(169,237)(170,223)
(171,222)(172,234)(173,233)(174,232)(175,231)(176,230)(177,229)(178,228)
(179,227)(180,226)(181,225)(182,224)(183,210)(184,209)(185,221)(186,220)
(187,219)(188,218)(189,217)(190,216)(191,215)(192,214)(193,213)(194,212)
(195,211);;
s2 := (  1,144)(  2,145)(  3,146)(  4,147)(  5,148)(  6,149)(  7,150)(  8,151)
(  9,152)( 10,153)( 11,154)( 12,155)( 13,156)( 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)( 27,183)( 28,184)( 29,185)( 30,186)( 31,187)( 32,188)
( 33,189)( 34,190)( 35,191)( 36,192)( 37,193)( 38,194)( 39,195)( 40,170)
( 41,171)( 42,172)( 43,173)( 44,174)( 45,175)( 46,176)( 47,177)( 48,178)
( 49,179)( 50,180)( 51,181)( 52,182)( 53,157)( 54,158)( 55,159)( 56,160)
( 57,161)( 58,162)( 59,163)( 60,164)( 61,165)( 62,166)( 63,167)( 64,168)
( 65,169)( 66,209)( 67,210)( 68,211)( 69,212)( 70,213)( 71,214)( 72,215)
( 73,216)( 74,217)( 75,218)( 76,219)( 77,220)( 78,221)( 79,196)( 80,197)
( 81,198)( 82,199)( 83,200)( 84,201)( 85,202)( 86,203)( 87,204)( 88,205)
( 89,206)( 90,207)( 91,208)( 92,248)( 93,249)( 94,250)( 95,251)( 96,252)
( 97,253)( 98,254)( 99,255)(100,256)(101,257)(102,258)(103,259)(104,260)
(105,235)(106,236)(107,237)(108,238)(109,239)(110,240)(111,241)(112,242)
(113,243)(114,244)(115,245)(116,246)(117,247)(118,222)(119,223)(120,224)
(121,225)(122,226)(123,227)(124,228)(125,229)(126,230)(127,231)(128,232)
(129,233)(130,234);;
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, 
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(260)!(  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);
s1 := Sym(260)!(  1,  2)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 14, 54)
( 15, 53)( 16, 65)( 17, 64)( 18, 63)( 19, 62)( 20, 61)( 21, 60)( 22, 59)
( 23, 58)( 24, 57)( 25, 56)( 26, 55)( 27, 41)( 28, 40)( 29, 52)( 30, 51)
( 31, 50)( 32, 49)( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)
( 39, 42)( 66, 67)( 68, 78)( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 79,119)
( 80,118)( 81,130)( 82,129)( 83,128)( 84,127)( 85,126)( 86,125)( 87,124)
( 88,123)( 89,122)( 90,121)( 91,120)( 92,106)( 93,105)( 94,117)( 95,116)
( 96,115)( 97,114)( 98,113)( 99,112)(100,111)(101,110)(102,109)(103,108)
(104,107)(131,197)(132,196)(133,208)(134,207)(135,206)(136,205)(137,204)
(138,203)(139,202)(140,201)(141,200)(142,199)(143,198)(144,249)(145,248)
(146,260)(147,259)(148,258)(149,257)(150,256)(151,255)(152,254)(153,253)
(154,252)(155,251)(156,250)(157,236)(158,235)(159,247)(160,246)(161,245)
(162,244)(163,243)(164,242)(165,241)(166,240)(167,239)(168,238)(169,237)
(170,223)(171,222)(172,234)(173,233)(174,232)(175,231)(176,230)(177,229)
(178,228)(179,227)(180,226)(181,225)(182,224)(183,210)(184,209)(185,221)
(186,220)(187,219)(188,218)(189,217)(190,216)(191,215)(192,214)(193,213)
(194,212)(195,211);
s2 := Sym(260)!(  1,144)(  2,145)(  3,146)(  4,147)(  5,148)(  6,149)(  7,150)
(  8,151)(  9,152)( 10,153)( 11,154)( 12,155)( 13,156)( 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)( 27,183)( 28,184)( 29,185)( 30,186)( 31,187)
( 32,188)( 33,189)( 34,190)( 35,191)( 36,192)( 37,193)( 38,194)( 39,195)
( 40,170)( 41,171)( 42,172)( 43,173)( 44,174)( 45,175)( 46,176)( 47,177)
( 48,178)( 49,179)( 50,180)( 51,181)( 52,182)( 53,157)( 54,158)( 55,159)
( 56,160)( 57,161)( 58,162)( 59,163)( 60,164)( 61,165)( 62,166)( 63,167)
( 64,168)( 65,169)( 66,209)( 67,210)( 68,211)( 69,212)( 70,213)( 71,214)
( 72,215)( 73,216)( 74,217)( 75,218)( 76,219)( 77,220)( 78,221)( 79,196)
( 80,197)( 81,198)( 82,199)( 83,200)( 84,201)( 85,202)( 86,203)( 87,204)
( 88,205)( 89,206)( 90,207)( 91,208)( 92,248)( 93,249)( 94,250)( 95,251)
( 96,252)( 97,253)( 98,254)( 99,255)(100,256)(101,257)(102,258)(103,259)
(104,260)(105,235)(106,236)(107,237)(108,238)(109,239)(110,240)(111,241)
(112,242)(113,243)(114,244)(115,245)(116,246)(117,247)(118,222)(119,223)
(120,224)(121,225)(122,226)(123,227)(124,228)(125,229)(126,230)(127,231)
(128,232)(129,233)(130,234);
poly := sub<Sym(260)|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, 
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