Polytope of Type {98,6}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope