Polytope of Type {260,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {260,2}*1040
if this polytope has a name.
Group : SmallGroup(1040,204)
Rank : 3
Schlafli Type : {260,2}
Number of vertices, edges, etc : 260, 260, 2
Order of s₀s₁s₂ : 260
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {130,2}*520
   4-fold quotients : {65,2}*260
   5-fold quotients : {52,2}*208
   10-fold quotients : {26,2}*104
   13-fold quotients : {20,2}*80
   20-fold quotients : {13,2}*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 := (  2, 13)(  3, 12)(  4, 11)(  5, 10)(  6,  9)(  7,  8)( 14, 53)( 15, 65)
( 16, 64)( 17, 63)( 18, 62)( 19, 61)( 20, 60)( 21, 59)( 22, 58)( 23, 57)
( 24, 56)( 25, 55)( 26, 54)( 27, 40)( 28, 52)( 29, 51)( 30, 50)( 31, 49)
( 32, 48)( 33, 47)( 34, 46)( 35, 45)( 36, 44)( 37, 43)( 38, 42)( 39, 41)
( 67, 78)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79,118)( 80,130)
( 81,129)( 82,128)( 83,127)( 84,126)( 85,125)( 86,124)( 87,123)( 88,122)
( 89,121)( 90,120)( 91,119)( 92,105)( 93,117)( 94,116)( 95,115)( 96,114)
( 97,113)( 98,112)( 99,111)(100,110)(101,109)(102,108)(103,107)(104,106)
(131,196)(132,208)(133,207)(134,206)(135,205)(136,204)(137,203)(138,202)
(139,201)(140,200)(141,199)(142,198)(143,197)(144,248)(145,260)(146,259)
(147,258)(148,257)(149,256)(150,255)(151,254)(152,253)(153,252)(154,251)
(155,250)(156,249)(157,235)(158,247)(159,246)(160,245)(161,244)(162,243)
(163,242)(164,241)(165,240)(166,239)(167,238)(168,237)(169,236)(170,222)
(171,234)(172,233)(173,232)(174,231)(175,230)(176,229)(177,228)(178,227)
(179,226)(180,225)(181,224)(182,223)(183,209)(184,221)(185,220)(186,219)
(187,218)(188,217)(189,216)(190,215)(191,214)(192,213)(193,212)(194,211)
(195,210);;
s1 := (  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)( 14,132)( 15,131)( 16,143)
( 17,142)( 18,141)( 19,140)( 20,139)( 21,138)( 22,137)( 23,136)( 24,135)
( 25,134)( 26,133)( 27,184)( 28,183)( 29,195)( 30,194)( 31,193)( 32,192)
( 33,191)( 34,190)( 35,189)( 36,188)( 37,187)( 38,186)( 39,185)( 40,171)
( 41,170)( 42,182)( 43,181)( 44,180)( 45,179)( 46,178)( 47,177)( 48,176)
( 49,175)( 50,174)( 51,173)( 52,172)( 53,158)( 54,157)( 55,169)( 56,168)
( 57,167)( 58,166)( 59,165)( 60,164)( 61,163)( 62,162)( 63,161)( 64,160)
( 65,159)( 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)( 79,197)( 80,196)
( 81,208)( 82,207)( 83,206)( 84,205)( 85,204)( 86,203)( 87,202)( 88,201)
( 89,200)( 90,199)( 91,198)( 92,249)( 93,248)( 94,260)( 95,259)( 96,258)
( 97,257)( 98,256)( 99,255)(100,254)(101,253)(102,252)(103,251)(104,250)
(105,236)(106,235)(107,247)(108,246)(109,245)(110,244)(111,243)(112,242)
(113,241)(114,240)(115,239)(116,238)(117,237)(118,223)(119,222)(120,234)
(121,233)(122,232)(123,231)(124,230)(125,229)(126,228)(127,227)(128,226)
(129,225)(130,224);;
s2 := (261,262);;
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, 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*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*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*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*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*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*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*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*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*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(262)!(  2, 13)(  3, 12)(  4, 11)(  5, 10)(  6,  9)(  7,  8)( 14, 53)
( 15, 65)( 16, 64)( 17, 63)( 18, 62)( 19, 61)( 20, 60)( 21, 59)( 22, 58)
( 23, 57)( 24, 56)( 25, 55)( 26, 54)( 27, 40)( 28, 52)( 29, 51)( 30, 50)
( 31, 49)( 32, 48)( 33, 47)( 34, 46)( 35, 45)( 36, 44)( 37, 43)( 38, 42)
( 39, 41)( 67, 78)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79,118)
( 80,130)( 81,129)( 82,128)( 83,127)( 84,126)( 85,125)( 86,124)( 87,123)
( 88,122)( 89,121)( 90,120)( 91,119)( 92,105)( 93,117)( 94,116)( 95,115)
( 96,114)( 97,113)( 98,112)( 99,111)(100,110)(101,109)(102,108)(103,107)
(104,106)(131,196)(132,208)(133,207)(134,206)(135,205)(136,204)(137,203)
(138,202)(139,201)(140,200)(141,199)(142,198)(143,197)(144,248)(145,260)
(146,259)(147,258)(148,257)(149,256)(150,255)(151,254)(152,253)(153,252)
(154,251)(155,250)(156,249)(157,235)(158,247)(159,246)(160,245)(161,244)
(162,243)(163,242)(164,241)(165,240)(166,239)(167,238)(168,237)(169,236)
(170,222)(171,234)(172,233)(173,232)(174,231)(175,230)(176,229)(177,228)
(178,227)(179,226)(180,225)(181,224)(182,223)(183,209)(184,221)(185,220)
(186,219)(187,218)(188,217)(189,216)(190,215)(191,214)(192,213)(193,212)
(194,211)(195,210);
s1 := Sym(262)!(  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)( 14,132)( 15,131)
( 16,143)( 17,142)( 18,141)( 19,140)( 20,139)( 21,138)( 22,137)( 23,136)
( 24,135)( 25,134)( 26,133)( 27,184)( 28,183)( 29,195)( 30,194)( 31,193)
( 32,192)( 33,191)( 34,190)( 35,189)( 36,188)( 37,187)( 38,186)( 39,185)
( 40,171)( 41,170)( 42,182)( 43,181)( 44,180)( 45,179)( 46,178)( 47,177)
( 48,176)( 49,175)( 50,174)( 51,173)( 52,172)( 53,158)( 54,157)( 55,169)
( 56,168)( 57,167)( 58,166)( 59,165)( 60,164)( 61,163)( 62,162)( 63,161)
( 64,160)( 65,159)( 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)( 79,197)
( 80,196)( 81,208)( 82,207)( 83,206)( 84,205)( 85,204)( 86,203)( 87,202)
( 88,201)( 89,200)( 90,199)( 91,198)( 92,249)( 93,248)( 94,260)( 95,259)
( 96,258)( 97,257)( 98,256)( 99,255)(100,254)(101,253)(102,252)(103,251)
(104,250)(105,236)(106,235)(107,247)(108,246)(109,245)(110,244)(111,243)
(112,242)(113,241)(114,240)(115,239)(116,238)(117,237)(118,223)(119,222)
(120,234)(121,233)(122,232)(123,231)(124,230)(125,229)(126,228)(127,227)
(128,226)(129,225)(130,224);
s2 := Sym(262)!(261,262);
poly := sub<Sym(262)|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, 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*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*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*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*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*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*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*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*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*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 >;

to this polytope