Polytope of Type {6,98}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,98}*1176
Also Known As : {6,98|2}. if this polytope has another name.
Group : SmallGroup(1176,49)
Rank : 3
Schlafli Type : {6,98}
Number of vertices, edges, etc : 6, 294, 98
Order of s₀s₁s₂ : 294
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 : {2,98}*392
   6-fold quotients : {2,49}*196
   7-fold quotients : {6,14}*168
   21-fold quotients : {2,14}*56
   42-fold quotients : {2,7}*28
   49-fold quotients : {6,2}*24
   98-fold quotients : {3,2}*12
   147-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope