Polytope of Type {4,130}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,130}*1040
Also Known As : {4,130|2}. if this polytope has another name.
Group : SmallGroup(1040,206)
Rank : 3
Schlafli Type : {4,130}
Number of vertices, edges, etc : 4, 260, 130
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 : {2,130}*520
   4-fold quotients : {2,65}*260
   5-fold quotients : {4,26}*208
   10-fold quotients : {2,26}*104
   13-fold quotients : {4,10}*80
   20-fold quotients : {2,13}*52
   26-fold quotients : {2,10}*40
   52-fold quotients : {2,5}*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 := (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)(144,209)(145,210)(146,211)
(147,212)(148,213)(149,214)(150,215)(151,216)(152,217)(153,218)(154,219)
(155,220)(156,221)(157,222)(158,223)(159,224)(160,225)(161,226)(162,227)
(163,228)(164,229)(165,230)(166,231)(167,232)(168,233)(169,234)(170,235)
(171,236)(172,237)(173,238)(174,239)(175,240)(176,241)(177,242)(178,243)
(179,244)(180,245)(181,246)(182,247)(183,248)(184,249)(185,250)(186,251)
(187,252)(188,253)(189,254)(190,255)(191,256)(192,257)(193,258)(194,259)
(195,260);;
s1 := (  1,131)(  2,143)(  3,142)(  4,141)(  5,140)(  6,139)(  7,138)(  8,137)
(  9,136)( 10,135)( 11,134)( 12,133)( 13,132)( 14,183)( 15,195)( 16,194)
( 17,193)( 18,192)( 19,191)( 20,190)( 21,189)( 22,188)( 23,187)( 24,186)
( 25,185)( 26,184)( 27,170)( 28,182)( 29,181)( 30,180)( 31,179)( 32,178)
( 33,177)( 34,176)( 35,175)( 36,174)( 37,173)( 38,172)( 39,171)( 40,157)
( 41,169)( 42,168)( 43,167)( 44,166)( 45,165)( 46,164)( 47,163)( 48,162)
( 49,161)( 50,160)( 51,159)( 52,158)( 53,144)( 54,156)( 55,155)( 56,154)
( 57,153)( 58,152)( 59,151)( 60,150)( 61,149)( 62,148)( 63,147)( 64,146)
( 65,145)( 66,196)( 67,208)( 68,207)( 69,206)( 70,205)( 71,204)( 72,203)
( 73,202)( 74,201)( 75,200)( 76,199)( 77,198)( 78,197)( 79,248)( 80,260)
( 81,259)( 82,258)( 83,257)( 84,256)( 85,255)( 86,254)( 87,253)( 88,252)
( 89,251)( 90,250)( 91,249)( 92,235)( 93,247)( 94,246)( 95,245)( 96,244)
( 97,243)( 98,242)( 99,241)(100,240)(101,239)(102,238)(103,237)(104,236)
(105,222)(106,234)(107,233)(108,232)(109,231)(110,230)(111,229)(112,228)
(113,227)(114,226)(115,225)(116,224)(117,223)(118,209)(119,221)(120,220)
(121,219)(122,218)(123,217)(124,216)(125,215)(126,214)(127,213)(128,212)
(129,211)(130,210);;
s2 := (  1, 15)(  2, 14)(  3, 26)(  4, 25)(  5, 24)(  6, 23)(  7, 22)(  8, 21)
(  9, 20)( 10, 19)( 11, 18)( 12, 17)( 13, 16)( 27, 54)( 28, 53)( 29, 65)
( 30, 64)( 31, 63)( 32, 62)( 33, 61)( 34, 60)( 35, 59)( 36, 58)( 37, 57)
( 38, 56)( 39, 55)( 40, 41)( 42, 52)( 43, 51)( 44, 50)( 45, 49)( 46, 48)
( 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)( 92,119)( 93,118)( 94,130)
( 95,129)( 96,128)( 97,127)( 98,126)( 99,125)(100,124)(101,123)(102,122)
(103,121)(104,120)(105,106)(107,117)(108,116)(109,115)(110,114)(111,113)
(131,145)(132,144)(133,156)(134,155)(135,154)(136,153)(137,152)(138,151)
(139,150)(140,149)(141,148)(142,147)(143,146)(157,184)(158,183)(159,195)
(160,194)(161,193)(162,192)(163,191)(164,190)(165,189)(166,188)(167,187)
(168,186)(169,185)(170,171)(172,182)(173,181)(174,180)(175,179)(176,178)
(196,210)(197,209)(198,221)(199,220)(200,219)(201,218)(202,217)(203,216)
(204,215)(205,214)(206,213)(207,212)(208,211)(222,249)(223,248)(224,260)
(225,259)(226,258)(227,257)(228,256)(229,255)(230,254)(231,253)(232,252)
(233,251)(234,250)(235,236)(237,247)(238,246)(239,245)(240,244)(241,243);;
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*s0*s1*s0*s1*s0*s1, 
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*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*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*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*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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope