Polytope of Type {258,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {258,2}*1032
if this polytope has a name.
Group : SmallGroup(1032,53)
Rank : 3
Schlafli Type : {258,2}
Number of vertices, edges, etc : 258, 258, 2
Order of s₀s₁s₂ : 258
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 : {129,2}*516
   3-fold quotients : {86,2}*344
   6-fold quotients : {43,2}*172
   43-fold quotients : {6,2}*24
   86-fold quotients : {3,2}*12
   129-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope