Polytope of Type {6,106}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,106}*1272
Also Known As : {6,106|2}. if this polytope has another name.
Group : SmallGroup(1272,39)
Rank : 3
Schlafli Type : {6,106}
Number of vertices, edges, etc : 6, 318, 106
Order of s₀s₁s₂ : 318
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) :
   3-fold quotients : {2,106}*424
   6-fold quotients : {2,53}*212
   53-fold quotients : {6,2}*24
   106-fold quotients : {3,2}*12
   159-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 54,107)( 55,108)( 56,109)( 57,110)( 58,111)( 59,112)( 60,113)( 61,114)
( 62,115)( 63,116)( 64,117)( 65,118)( 66,119)( 67,120)( 68,121)( 69,122)
( 70,123)( 71,124)( 72,125)( 73,126)( 74,127)( 75,128)( 76,129)( 77,130)
( 78,131)( 79,132)( 80,133)( 81,134)( 82,135)( 83,136)( 84,137)( 85,138)
( 86,139)( 87,140)( 88,141)( 89,142)( 90,143)( 91,144)( 92,145)( 93,146)
( 94,147)( 95,148)( 96,149)( 97,150)( 98,151)( 99,152)(100,153)(101,154)
(102,155)(103,156)(104,157)(105,158)(106,159)(213,266)(214,267)(215,268)
(216,269)(217,270)(218,271)(219,272)(220,273)(221,274)(222,275)(223,276)
(224,277)(225,278)(226,279)(227,280)(228,281)(229,282)(230,283)(231,284)
(232,285)(233,286)(234,287)(235,288)(236,289)(237,290)(238,291)(239,292)
(240,293)(241,294)(242,295)(243,296)(244,297)(245,298)(246,299)(247,300)
(248,301)(249,302)(250,303)(251,304)(252,305)(253,306)(254,307)(255,308)
(256,309)(257,310)(258,311)(259,312)(260,313)(261,314)(262,315)(263,316)
(264,317)(265,318);;
s1 := (  1, 54)(  2,106)(  3,105)(  4,104)(  5,103)(  6,102)(  7,101)(  8,100)
(  9, 99)( 10, 98)( 11, 97)( 12, 96)( 13, 95)( 14, 94)( 15, 93)( 16, 92)
( 17, 91)( 18, 90)( 19, 89)( 20, 88)( 21, 87)( 22, 86)( 23, 85)( 24, 84)
( 25, 83)( 26, 82)( 27, 81)( 28, 80)( 29, 79)( 30, 78)( 31, 77)( 32, 76)
( 33, 75)( 34, 74)( 35, 73)( 36, 72)( 37, 71)( 38, 70)( 39, 69)( 40, 68)
( 41, 67)( 42, 66)( 43, 65)( 44, 64)( 45, 63)( 46, 62)( 47, 61)( 48, 60)
( 49, 59)( 50, 58)( 51, 57)( 52, 56)( 53, 55)(108,159)(109,158)(110,157)
(111,156)(112,155)(113,154)(114,153)(115,152)(116,151)(117,150)(118,149)
(119,148)(120,147)(121,146)(122,145)(123,144)(124,143)(125,142)(126,141)
(127,140)(128,139)(129,138)(130,137)(131,136)(132,135)(133,134)(160,213)
(161,265)(162,264)(163,263)(164,262)(165,261)(166,260)(167,259)(168,258)
(169,257)(170,256)(171,255)(172,254)(173,253)(174,252)(175,251)(176,250)
(177,249)(178,248)(179,247)(180,246)(181,245)(182,244)(183,243)(184,242)
(185,241)(186,240)(187,239)(188,238)(189,237)(190,236)(191,235)(192,234)
(193,233)(194,232)(195,231)(196,230)(197,229)(198,228)(199,227)(200,226)
(201,225)(202,224)(203,223)(204,222)(205,221)(206,220)(207,219)(208,218)
(209,217)(210,216)(211,215)(212,214)(267,318)(268,317)(269,316)(270,315)
(271,314)(272,313)(273,312)(274,311)(275,310)(276,309)(277,308)(278,307)
(279,306)(280,305)(281,304)(282,303)(283,302)(284,301)(285,300)(286,299)
(287,298)(288,297)(289,296)(290,295)(291,294)(292,293);;
s2 := (  1,161)(  2,160)(  3,212)(  4,211)(  5,210)(  6,209)(  7,208)(  8,207)
(  9,206)( 10,205)( 11,204)( 12,203)( 13,202)( 14,201)( 15,200)( 16,199)
( 17,198)( 18,197)( 19,196)( 20,195)( 21,194)( 22,193)( 23,192)( 24,191)
( 25,190)( 26,189)( 27,188)( 28,187)( 29,186)( 30,185)( 31,184)( 32,183)
( 33,182)( 34,181)( 35,180)( 36,179)( 37,178)( 38,177)( 39,176)( 40,175)
( 41,174)( 42,173)( 43,172)( 44,171)( 45,170)( 46,169)( 47,168)( 48,167)
( 49,166)( 50,165)( 51,164)( 52,163)( 53,162)( 54,214)( 55,213)( 56,265)
( 57,264)( 58,263)( 59,262)( 60,261)( 61,260)( 62,259)( 63,258)( 64,257)
( 65,256)( 66,255)( 67,254)( 68,253)( 69,252)( 70,251)( 71,250)( 72,249)
( 73,248)( 74,247)( 75,246)( 76,245)( 77,244)( 78,243)( 79,242)( 80,241)
( 81,240)( 82,239)( 83,238)( 84,237)( 85,236)( 86,235)( 87,234)( 88,233)
( 89,232)( 90,231)( 91,230)( 92,229)( 93,228)( 94,227)( 95,226)( 96,225)
( 97,224)( 98,223)( 99,222)(100,221)(101,220)(102,219)(103,218)(104,217)
(105,216)(106,215)(107,267)(108,266)(109,318)(110,317)(111,316)(112,315)
(113,314)(114,313)(115,312)(116,311)(117,310)(118,309)(119,308)(120,307)
(121,306)(122,305)(123,304)(124,303)(125,302)(126,301)(127,300)(128,299)
(129,298)(130,297)(131,296)(132,295)(133,294)(134,293)(135,292)(136,291)
(137,290)(138,289)(139,288)(140,287)(141,286)(142,285)(143,284)(144,283)
(145,282)(146,281)(147,280)(148,279)(149,278)(150,277)(151,276)(152,275)
(153,274)(154,273)(155,272)(156,271)(157,270)(158,269)(159,268);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(318)!( 54,107)( 55,108)( 56,109)( 57,110)( 58,111)( 59,112)( 60,113)
( 61,114)( 62,115)( 63,116)( 64,117)( 65,118)( 66,119)( 67,120)( 68,121)
( 69,122)( 70,123)( 71,124)( 72,125)( 73,126)( 74,127)( 75,128)( 76,129)
( 77,130)( 78,131)( 79,132)( 80,133)( 81,134)( 82,135)( 83,136)( 84,137)
( 85,138)( 86,139)( 87,140)( 88,141)( 89,142)( 90,143)( 91,144)( 92,145)
( 93,146)( 94,147)( 95,148)( 96,149)( 97,150)( 98,151)( 99,152)(100,153)
(101,154)(102,155)(103,156)(104,157)(105,158)(106,159)(213,266)(214,267)
(215,268)(216,269)(217,270)(218,271)(219,272)(220,273)(221,274)(222,275)
(223,276)(224,277)(225,278)(226,279)(227,280)(228,281)(229,282)(230,283)
(231,284)(232,285)(233,286)(234,287)(235,288)(236,289)(237,290)(238,291)
(239,292)(240,293)(241,294)(242,295)(243,296)(244,297)(245,298)(246,299)
(247,300)(248,301)(249,302)(250,303)(251,304)(252,305)(253,306)(254,307)
(255,308)(256,309)(257,310)(258,311)(259,312)(260,313)(261,314)(262,315)
(263,316)(264,317)(265,318);
s1 := Sym(318)!(  1, 54)(  2,106)(  3,105)(  4,104)(  5,103)(  6,102)(  7,101)
(  8,100)(  9, 99)( 10, 98)( 11, 97)( 12, 96)( 13, 95)( 14, 94)( 15, 93)
( 16, 92)( 17, 91)( 18, 90)( 19, 89)( 20, 88)( 21, 87)( 22, 86)( 23, 85)
( 24, 84)( 25, 83)( 26, 82)( 27, 81)( 28, 80)( 29, 79)( 30, 78)( 31, 77)
( 32, 76)( 33, 75)( 34, 74)( 35, 73)( 36, 72)( 37, 71)( 38, 70)( 39, 69)
( 40, 68)( 41, 67)( 42, 66)( 43, 65)( 44, 64)( 45, 63)( 46, 62)( 47, 61)
( 48, 60)( 49, 59)( 50, 58)( 51, 57)( 52, 56)( 53, 55)(108,159)(109,158)
(110,157)(111,156)(112,155)(113,154)(114,153)(115,152)(116,151)(117,150)
(118,149)(119,148)(120,147)(121,146)(122,145)(123,144)(124,143)(125,142)
(126,141)(127,140)(128,139)(129,138)(130,137)(131,136)(132,135)(133,134)
(160,213)(161,265)(162,264)(163,263)(164,262)(165,261)(166,260)(167,259)
(168,258)(169,257)(170,256)(171,255)(172,254)(173,253)(174,252)(175,251)
(176,250)(177,249)(178,248)(179,247)(180,246)(181,245)(182,244)(183,243)
(184,242)(185,241)(186,240)(187,239)(188,238)(189,237)(190,236)(191,235)
(192,234)(193,233)(194,232)(195,231)(196,230)(197,229)(198,228)(199,227)
(200,226)(201,225)(202,224)(203,223)(204,222)(205,221)(206,220)(207,219)
(208,218)(209,217)(210,216)(211,215)(212,214)(267,318)(268,317)(269,316)
(270,315)(271,314)(272,313)(273,312)(274,311)(275,310)(276,309)(277,308)
(278,307)(279,306)(280,305)(281,304)(282,303)(283,302)(284,301)(285,300)
(286,299)(287,298)(288,297)(289,296)(290,295)(291,294)(292,293);
s2 := Sym(318)!(  1,161)(  2,160)(  3,212)(  4,211)(  5,210)(  6,209)(  7,208)
(  8,207)(  9,206)( 10,205)( 11,204)( 12,203)( 13,202)( 14,201)( 15,200)
( 16,199)( 17,198)( 18,197)( 19,196)( 20,195)( 21,194)( 22,193)( 23,192)
( 24,191)( 25,190)( 26,189)( 27,188)( 28,187)( 29,186)( 30,185)( 31,184)
( 32,183)( 33,182)( 34,181)( 35,180)( 36,179)( 37,178)( 38,177)( 39,176)
( 40,175)( 41,174)( 42,173)( 43,172)( 44,171)( 45,170)( 46,169)( 47,168)
( 48,167)( 49,166)( 50,165)( 51,164)( 52,163)( 53,162)( 54,214)( 55,213)
( 56,265)( 57,264)( 58,263)( 59,262)( 60,261)( 61,260)( 62,259)( 63,258)
( 64,257)( 65,256)( 66,255)( 67,254)( 68,253)( 69,252)( 70,251)( 71,250)
( 72,249)( 73,248)( 74,247)( 75,246)( 76,245)( 77,244)( 78,243)( 79,242)
( 80,241)( 81,240)( 82,239)( 83,238)( 84,237)( 85,236)( 86,235)( 87,234)
( 88,233)( 89,232)( 90,231)( 91,230)( 92,229)( 93,228)( 94,227)( 95,226)
( 96,225)( 97,224)( 98,223)( 99,222)(100,221)(101,220)(102,219)(103,218)
(104,217)(105,216)(106,215)(107,267)(108,266)(109,318)(110,317)(111,316)
(112,315)(113,314)(114,313)(115,312)(116,311)(117,310)(118,309)(119,308)
(120,307)(121,306)(122,305)(123,304)(124,303)(125,302)(126,301)(127,300)
(128,299)(129,298)(130,297)(131,296)(132,295)(133,294)(134,293)(135,292)
(136,291)(137,290)(138,289)(139,288)(140,287)(141,286)(142,285)(143,284)
(144,283)(145,282)(146,281)(147,280)(148,279)(149,278)(150,277)(151,276)
(152,275)(153,274)(154,273)(155,272)(156,271)(157,270)(158,269)(159,268);
poly := sub<Sym(318)|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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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 >;

References : None.
to this polytope