Polytope of Type {6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6}*1176b
if this polytope has a name.
Group : SmallGroup(1176,225)
Rank : 3
Schlafli Type : {6,6}
Number of vertices, edges, etc : 98, 294, 98
Order of s₀s₁s₂ : 14
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,6}*588
   147-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope