Polytope of Type {20,26}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,26}*1040
Also Known As : {20,26|2}. if this polytope has another name.
Group : SmallGroup(1040,166)
Rank : 3
Schlafli Type : {20,26}
Number of vertices, edges, etc : 20, 260, 26
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 : {10,26}*520
   5-fold quotients : {4,26}*208
   10-fold quotients : {2,26}*104
   13-fold quotients : {20,2}*80
   20-fold quotients : {2,13}*52
   26-fold quotients : {10,2}*40
   52-fold quotients : {5,2}*20
   65-fold quotients : {4,2}*16
   130-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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