Polytope of Type {129,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {129,6}*1548
if this polytope has a name.
Group : SmallGroup(1548,36)
Rank : 3
Schlafli Type : {129,6}
Number of vertices, edges, etc : 129, 387, 6
Order of s₀s₁s₂ : 258
Order of s₀s₁s₂s₁ : 6
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) :
   3-fold quotients : {129,2}*516
   9-fold quotients : {43,2}*172
   43-fold quotients : {3,6}*36
   129-fold quotients : {3,2}*12
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)
(130,259)(131,301)(132,300)(133,299)(134,298)(135,297)(136,296)(137,295)
(138,294)(139,293)(140,292)(141,291)(142,290)(143,289)(144,288)(145,287)
(146,286)(147,285)(148,284)(149,283)(150,282)(151,281)(152,280)(153,279)
(154,278)(155,277)(156,276)(157,275)(158,274)(159,273)(160,272)(161,271)
(162,270)(163,269)(164,268)(165,267)(166,266)(167,265)(168,264)(169,263)
(170,262)(171,261)(172,260)(173,345)(174,387)(175,386)(176,385)(177,384)
(178,383)(179,382)(180,381)(181,380)(182,379)(183,378)(184,377)(185,376)
(186,375)(187,374)(188,373)(189,372)(190,371)(191,370)(192,369)(193,368)
(194,367)(195,366)(196,365)(197,364)(198,363)(199,362)(200,361)(201,360)
(202,359)(203,358)(204,357)(205,356)(206,355)(207,354)(208,353)(209,352)
(210,351)(211,350)(212,349)(213,348)(214,347)(215,346)(216,302)(217,344)
(218,343)(219,342)(220,341)(221,340)(222,339)(223,338)(224,337)(225,336)
(226,335)(227,334)(228,333)(229,332)(230,331)(231,330)(232,329)(233,328)
(234,327)(235,326)(236,325)(237,324)(238,323)(239,322)(240,321)(241,320)
(242,319)(243,318)(244,317)(245,316)(246,315)(247,314)(248,313)(249,312)
(250,311)(251,310)(252,309)(253,308)(254,307)(255,306)(256,305)(257,304)
(258,303);;
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)(259,303)(260,302)(261,344)(262,343)(263,342)(264,341)(265,340)
(266,339)(267,338)(268,337)(269,336)(270,335)(271,334)(272,333)(273,332)
(274,331)(275,330)(276,329)(277,328)(278,327)(279,326)(280,325)(281,324)
(282,323)(283,322)(284,321)(285,320)(286,319)(287,318)(288,317)(289,316)
(290,315)(291,314)(292,313)(293,312)(294,311)(295,310)(296,309)(297,308)
(298,307)(299,306)(300,305)(301,304)(345,346)(347,387)(348,386)(349,385)
(350,384)(351,383)(352,382)(353,381)(354,380)(355,379)(356,378)(357,377)
(358,376)(359,375)(360,374)(361,373)(362,372)(363,371)(364,370)(365,369)
(366,368);;
s2 := ( 44, 87)( 45, 88)( 46, 89)( 47, 90)( 48, 91)( 49, 92)( 50, 93)( 51, 94)
( 52, 95)( 53, 96)( 54, 97)( 55, 98)( 56, 99)( 57,100)( 58,101)( 59,102)
( 60,103)( 61,104)( 62,105)( 63,106)( 64,107)( 65,108)( 66,109)( 67,110)
( 68,111)( 69,112)( 70,113)( 71,114)( 72,115)( 73,116)( 74,117)( 75,118)
( 76,119)( 77,120)( 78,121)( 79,122)( 80,123)( 81,124)( 82,125)( 83,126)
( 84,127)( 85,128)( 86,129)(173,216)(174,217)(175,218)(176,219)(177,220)
(178,221)(179,222)(180,223)(181,224)(182,225)(183,226)(184,227)(185,228)
(186,229)(187,230)(188,231)(189,232)(190,233)(191,234)(192,235)(193,236)
(194,237)(195,238)(196,239)(197,240)(198,241)(199,242)(200,243)(201,244)
(202,245)(203,246)(204,247)(205,248)(206,249)(207,250)(208,251)(209,252)
(210,253)(211,254)(212,255)(213,256)(214,257)(215,258)(302,345)(303,346)
(304,347)(305,348)(306,349)(307,350)(308,351)(309,352)(310,353)(311,354)
(312,355)(313,356)(314,357)(315,358)(316,359)(317,360)(318,361)(319,362)
(320,363)(321,364)(322,365)(323,366)(324,367)(325,368)(326,369)(327,370)
(328,371)(329,372)(330,373)(331,374)(332,375)(333,376)(334,377)(335,378)
(336,379)(337,380)(338,381)(339,382)(340,383)(341,384)(342,385)(343,386)
(344,387);;
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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(387)!(  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)(130,259)(131,301)(132,300)(133,299)(134,298)(135,297)(136,296)
(137,295)(138,294)(139,293)(140,292)(141,291)(142,290)(143,289)(144,288)
(145,287)(146,286)(147,285)(148,284)(149,283)(150,282)(151,281)(152,280)
(153,279)(154,278)(155,277)(156,276)(157,275)(158,274)(159,273)(160,272)
(161,271)(162,270)(163,269)(164,268)(165,267)(166,266)(167,265)(168,264)
(169,263)(170,262)(171,261)(172,260)(173,345)(174,387)(175,386)(176,385)
(177,384)(178,383)(179,382)(180,381)(181,380)(182,379)(183,378)(184,377)
(185,376)(186,375)(187,374)(188,373)(189,372)(190,371)(191,370)(192,369)
(193,368)(194,367)(195,366)(196,365)(197,364)(198,363)(199,362)(200,361)
(201,360)(202,359)(203,358)(204,357)(205,356)(206,355)(207,354)(208,353)
(209,352)(210,351)(211,350)(212,349)(213,348)(214,347)(215,346)(216,302)
(217,344)(218,343)(219,342)(220,341)(221,340)(222,339)(223,338)(224,337)
(225,336)(226,335)(227,334)(228,333)(229,332)(230,331)(231,330)(232,329)
(233,328)(234,327)(235,326)(236,325)(237,324)(238,323)(239,322)(240,321)
(241,320)(242,319)(243,318)(244,317)(245,316)(246,315)(247,314)(248,313)
(249,312)(250,311)(251,310)(252,309)(253,308)(254,307)(255,306)(256,305)
(257,304)(258,303);
s1 := Sym(387)!(  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)(259,303)(260,302)(261,344)(262,343)(263,342)(264,341)
(265,340)(266,339)(267,338)(268,337)(269,336)(270,335)(271,334)(272,333)
(273,332)(274,331)(275,330)(276,329)(277,328)(278,327)(279,326)(280,325)
(281,324)(282,323)(283,322)(284,321)(285,320)(286,319)(287,318)(288,317)
(289,316)(290,315)(291,314)(292,313)(293,312)(294,311)(295,310)(296,309)
(297,308)(298,307)(299,306)(300,305)(301,304)(345,346)(347,387)(348,386)
(349,385)(350,384)(351,383)(352,382)(353,381)(354,380)(355,379)(356,378)
(357,377)(358,376)(359,375)(360,374)(361,373)(362,372)(363,371)(364,370)
(365,369)(366,368);
s2 := Sym(387)!( 44, 87)( 45, 88)( 46, 89)( 47, 90)( 48, 91)( 49, 92)( 50, 93)
( 51, 94)( 52, 95)( 53, 96)( 54, 97)( 55, 98)( 56, 99)( 57,100)( 58,101)
( 59,102)( 60,103)( 61,104)( 62,105)( 63,106)( 64,107)( 65,108)( 66,109)
( 67,110)( 68,111)( 69,112)( 70,113)( 71,114)( 72,115)( 73,116)( 74,117)
( 75,118)( 76,119)( 77,120)( 78,121)( 79,122)( 80,123)( 81,124)( 82,125)
( 83,126)( 84,127)( 85,128)( 86,129)(173,216)(174,217)(175,218)(176,219)
(177,220)(178,221)(179,222)(180,223)(181,224)(182,225)(183,226)(184,227)
(185,228)(186,229)(187,230)(188,231)(189,232)(190,233)(191,234)(192,235)
(193,236)(194,237)(195,238)(196,239)(197,240)(198,241)(199,242)(200,243)
(201,244)(202,245)(203,246)(204,247)(205,248)(206,249)(207,250)(208,251)
(209,252)(210,253)(211,254)(212,255)(213,256)(214,257)(215,258)(302,345)
(303,346)(304,347)(305,348)(306,349)(307,350)(308,351)(309,352)(310,353)
(311,354)(312,355)(313,356)(314,357)(315,358)(316,359)(317,360)(318,361)
(319,362)(320,363)(321,364)(322,365)(323,366)(324,367)(325,368)(326,369)
(327,370)(328,371)(329,372)(330,373)(331,374)(332,375)(333,376)(334,377)
(335,378)(336,379)(337,380)(338,381)(339,382)(340,383)(341,384)(342,385)
(343,386)(344,387);
poly := sub<Sym(387)|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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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