Polytope of Type {130,4}

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