Polytope of Type {6,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,14}*1176a
if this polytope has a name.
Group : SmallGroup(1176,225)
Rank : 3
Schlafli Type : {6,14}
Number of vertices, edges, etc : 42, 294, 98
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 14
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 : {6,14}*588
   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 := (  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, 50)(  2, 65)(  3, 80)(  4, 95)(  5, 61)(  6, 76)(  7, 91)(  8, 92)
(  9, 58)( 10, 73)( 11, 88)( 12, 54)( 13, 69)( 14, 84)( 15, 85)( 16, 51)
( 17, 66)( 18, 81)( 19, 96)( 20, 62)( 21, 77)( 22, 78)( 23, 93)( 24, 59)
( 25, 74)( 26, 89)( 27, 55)( 28, 70)( 29, 71)( 30, 86)( 31, 52)( 32, 67)
( 33, 82)( 34, 97)( 35, 63)( 36, 64)( 37, 79)( 38, 94)( 39, 60)( 40, 75)
( 41, 90)( 42, 56)( 43, 57)( 44, 72)( 45, 87)( 46, 53)( 47, 68)( 48, 83)
( 49, 98)(100,114)(101,129)(102,144)(103,110)(104,125)(105,140)(106,141)
(108,122)(109,137)(111,118)(112,133)(113,134)(116,130)(117,145)(119,126)
(120,127)(121,142)(124,138)(128,135)(132,146)(136,143)(148,197)(149,212)
(150,227)(151,242)(152,208)(153,223)(154,238)(155,239)(156,205)(157,220)
(158,235)(159,201)(160,216)(161,231)(162,232)(163,198)(164,213)(165,228)
(166,243)(167,209)(168,224)(169,225)(170,240)(171,206)(172,221)(173,236)
(174,202)(175,217)(176,218)(177,233)(178,199)(179,214)(180,229)(181,244)
(182,210)(183,211)(184,226)(185,241)(186,207)(187,222)(188,237)(189,203)
(190,204)(191,219)(192,234)(193,200)(194,215)(195,230)(196,245)(247,261)
(248,276)(249,291)(250,257)(251,272)(252,287)(253,288)(255,269)(256,284)
(258,265)(259,280)(260,281)(263,277)(264,292)(266,273)(267,274)(268,289)
(271,285)(275,282)(279,293)(283,290);;
s2 := (  1,158)(  2,157)(  3,156)(  4,155)(  5,161)(  6,160)(  7,159)(  8,151)
(  9,150)( 10,149)( 11,148)( 12,154)( 13,153)( 14,152)( 15,193)( 16,192)
( 17,191)( 18,190)( 19,196)( 20,195)( 21,194)( 22,186)( 23,185)( 24,184)
( 25,183)( 26,189)( 27,188)( 28,187)( 29,179)( 30,178)( 31,177)( 32,176)
( 33,182)( 34,181)( 35,180)( 36,172)( 37,171)( 38,170)( 39,169)( 40,175)
( 41,174)( 42,173)( 43,165)( 44,164)( 45,163)( 46,162)( 47,168)( 48,167)
( 49,166)( 50,207)( 51,206)( 52,205)( 53,204)( 54,210)( 55,209)( 56,208)
( 57,200)( 58,199)( 59,198)( 60,197)( 61,203)( 62,202)( 63,201)( 64,242)
( 65,241)( 66,240)( 67,239)( 68,245)( 69,244)( 70,243)( 71,235)( 72,234)
( 73,233)( 74,232)( 75,238)( 76,237)( 77,236)( 78,228)( 79,227)( 80,226)
( 81,225)( 82,231)( 83,230)( 84,229)( 85,221)( 86,220)( 87,219)( 88,218)
( 89,224)( 90,223)( 91,222)( 92,214)( 93,213)( 94,212)( 95,211)( 96,217)
( 97,216)( 98,215)( 99,256)(100,255)(101,254)(102,253)(103,259)(104,258)
(105,257)(106,249)(107,248)(108,247)(109,246)(110,252)(111,251)(112,250)
(113,291)(114,290)(115,289)(116,288)(117,294)(118,293)(119,292)(120,284)
(121,283)(122,282)(123,281)(124,287)(125,286)(126,285)(127,277)(128,276)
(129,275)(130,274)(131,280)(132,279)(133,278)(134,270)(135,269)(136,268)
(137,267)(138,273)(139,272)(140,271)(141,263)(142,262)(143,261)(144,260)
(145,266)(146,265)(147,264);;
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, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*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 ];;
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, 50)(  2, 65)(  3, 80)(  4, 95)(  5, 61)(  6, 76)(  7, 91)
(  8, 92)(  9, 58)( 10, 73)( 11, 88)( 12, 54)( 13, 69)( 14, 84)( 15, 85)
( 16, 51)( 17, 66)( 18, 81)( 19, 96)( 20, 62)( 21, 77)( 22, 78)( 23, 93)
( 24, 59)( 25, 74)( 26, 89)( 27, 55)( 28, 70)( 29, 71)( 30, 86)( 31, 52)
( 32, 67)( 33, 82)( 34, 97)( 35, 63)( 36, 64)( 37, 79)( 38, 94)( 39, 60)
( 40, 75)( 41, 90)( 42, 56)( 43, 57)( 44, 72)( 45, 87)( 46, 53)( 47, 68)
( 48, 83)( 49, 98)(100,114)(101,129)(102,144)(103,110)(104,125)(105,140)
(106,141)(108,122)(109,137)(111,118)(112,133)(113,134)(116,130)(117,145)
(119,126)(120,127)(121,142)(124,138)(128,135)(132,146)(136,143)(148,197)
(149,212)(150,227)(151,242)(152,208)(153,223)(154,238)(155,239)(156,205)
(157,220)(158,235)(159,201)(160,216)(161,231)(162,232)(163,198)(164,213)
(165,228)(166,243)(167,209)(168,224)(169,225)(170,240)(171,206)(172,221)
(173,236)(174,202)(175,217)(176,218)(177,233)(178,199)(179,214)(180,229)
(181,244)(182,210)(183,211)(184,226)(185,241)(186,207)(187,222)(188,237)
(189,203)(190,204)(191,219)(192,234)(193,200)(194,215)(195,230)(196,245)
(247,261)(248,276)(249,291)(250,257)(251,272)(252,287)(253,288)(255,269)
(256,284)(258,265)(259,280)(260,281)(263,277)(264,292)(266,273)(267,274)
(268,289)(271,285)(275,282)(279,293)(283,290);
s2 := Sym(294)!(  1,158)(  2,157)(  3,156)(  4,155)(  5,161)(  6,160)(  7,159)
(  8,151)(  9,150)( 10,149)( 11,148)( 12,154)( 13,153)( 14,152)( 15,193)
( 16,192)( 17,191)( 18,190)( 19,196)( 20,195)( 21,194)( 22,186)( 23,185)
( 24,184)( 25,183)( 26,189)( 27,188)( 28,187)( 29,179)( 30,178)( 31,177)
( 32,176)( 33,182)( 34,181)( 35,180)( 36,172)( 37,171)( 38,170)( 39,169)
( 40,175)( 41,174)( 42,173)( 43,165)( 44,164)( 45,163)( 46,162)( 47,168)
( 48,167)( 49,166)( 50,207)( 51,206)( 52,205)( 53,204)( 54,210)( 55,209)
( 56,208)( 57,200)( 58,199)( 59,198)( 60,197)( 61,203)( 62,202)( 63,201)
( 64,242)( 65,241)( 66,240)( 67,239)( 68,245)( 69,244)( 70,243)( 71,235)
( 72,234)( 73,233)( 74,232)( 75,238)( 76,237)( 77,236)( 78,228)( 79,227)
( 80,226)( 81,225)( 82,231)( 83,230)( 84,229)( 85,221)( 86,220)( 87,219)
( 88,218)( 89,224)( 90,223)( 91,222)( 92,214)( 93,213)( 94,212)( 95,211)
( 96,217)( 97,216)( 98,215)( 99,256)(100,255)(101,254)(102,253)(103,259)
(104,258)(105,257)(106,249)(107,248)(108,247)(109,246)(110,252)(111,251)
(112,250)(113,291)(114,290)(115,289)(116,288)(117,294)(118,293)(119,292)
(120,284)(121,283)(122,282)(123,281)(124,287)(125,286)(126,285)(127,277)
(128,276)(129,275)(130,274)(131,280)(132,279)(133,278)(134,270)(135,269)
(136,268)(137,267)(138,273)(139,272)(140,271)(141,263)(142,262)(143,261)
(144,260)(145,266)(146,265)(147,264);
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, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*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 >;

References : None.
to this polytope