Polytope of Type {42,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {42,14}*1176c
if this polytope has a name.
Group : SmallGroup(1176,265)
Rank : 3
Schlafli Type : {42,14}
Number of vertices, edges, etc : 42, 294, 14
Order of s₀s₁s₂ : 42
Order of s₀s₁s₂s₁ : 14
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
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 : {21,14}*588
   3-fold quotients : {14,14}*392c
   6-fold quotients : {7,14}*196
   7-fold quotients : {42,2}*168
   14-fold quotients : {21,2}*84
   21-fold quotients : {14,2}*56
   42-fold quotients : {7,2}*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 := (  2,  7)(  3,  6)(  4,  5)(  8, 43)(  9, 49)( 10, 48)( 11, 47)( 12, 46)
( 13, 45)( 14, 44)( 15, 36)( 16, 42)( 17, 41)( 18, 40)( 19, 39)( 20, 38)
( 21, 37)( 22, 29)( 23, 35)( 24, 34)( 25, 33)( 26, 32)( 27, 31)( 28, 30)
( 50, 99)( 51,105)( 52,104)( 53,103)( 54,102)( 55,101)( 56,100)( 57,141)
( 58,147)( 59,146)( 60,145)( 61,144)( 62,143)( 63,142)( 64,134)( 65,140)
( 66,139)( 67,138)( 68,137)( 69,136)( 70,135)( 71,127)( 72,133)( 73,132)
( 74,131)( 75,130)( 76,129)( 77,128)( 78,120)( 79,126)( 80,125)( 81,124)
( 82,123)( 83,122)( 84,121)( 85,113)( 86,119)( 87,118)( 88,117)( 89,116)
( 90,115)( 91,114)( 92,106)( 93,112)( 94,111)( 95,110)( 96,109)( 97,108)
( 98,107)(149,154)(150,153)(151,152)(155,190)(156,196)(157,195)(158,194)
(159,193)(160,192)(161,191)(162,183)(163,189)(164,188)(165,187)(166,186)
(167,185)(168,184)(169,176)(170,182)(171,181)(172,180)(173,179)(174,178)
(175,177)(197,246)(198,252)(199,251)(200,250)(201,249)(202,248)(203,247)
(204,288)(205,294)(206,293)(207,292)(208,291)(209,290)(210,289)(211,281)
(212,287)(213,286)(214,285)(215,284)(216,283)(217,282)(218,274)(219,280)
(220,279)(221,278)(222,277)(223,276)(224,275)(225,267)(226,273)(227,272)
(228,271)(229,270)(230,269)(231,268)(232,260)(233,266)(234,265)(235,264)
(236,263)(237,262)(238,261)(239,253)(240,259)(241,258)(242,257)(243,256)
(244,255)(245,254);;
s1 := (  1,205)(  2,204)(  3,210)(  4,209)(  5,208)(  6,207)(  7,206)(  8,198)
(  9,197)( 10,203)( 11,202)( 12,201)( 13,200)( 14,199)( 15,240)( 16,239)
( 17,245)( 18,244)( 19,243)( 20,242)( 21,241)( 22,233)( 23,232)( 24,238)
( 25,237)( 26,236)( 27,235)( 28,234)( 29,226)( 30,225)( 31,231)( 32,230)
( 33,229)( 34,228)( 35,227)( 36,219)( 37,218)( 38,224)( 39,223)( 40,222)
( 41,221)( 42,220)( 43,212)( 44,211)( 45,217)( 46,216)( 47,215)( 48,214)
( 49,213)( 50,156)( 51,155)( 52,161)( 53,160)( 54,159)( 55,158)( 56,157)
( 57,149)( 58,148)( 59,154)( 60,153)( 61,152)( 62,151)( 63,150)( 64,191)
( 65,190)( 66,196)( 67,195)( 68,194)( 69,193)( 70,192)( 71,184)( 72,183)
( 73,189)( 74,188)( 75,187)( 76,186)( 77,185)( 78,177)( 79,176)( 80,182)
( 81,181)( 82,180)( 83,179)( 84,178)( 85,170)( 86,169)( 87,175)( 88,174)
( 89,173)( 90,172)( 91,171)( 92,163)( 93,162)( 94,168)( 95,167)( 96,166)
( 97,165)( 98,164)( 99,254)(100,253)(101,259)(102,258)(103,257)(104,256)
(105,255)(106,247)(107,246)(108,252)(109,251)(110,250)(111,249)(112,248)
(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);;
s2 := (  2,  7)(  3,  6)(  4,  5)(  9, 14)( 10, 13)( 11, 12)( 16, 21)( 17, 20)
( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 30, 35)( 31, 34)( 32, 33)( 37, 42)
( 38, 41)( 39, 40)( 44, 49)( 45, 48)( 46, 47)( 51, 56)( 52, 55)( 53, 54)
( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)( 72, 77)( 73, 76)
( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 86, 91)( 87, 90)( 88, 89)( 93, 98)
( 94, 97)( 95, 96)(100,105)(101,104)(102,103)(107,112)(108,111)(109,110)
(114,119)(115,118)(116,117)(121,126)(122,125)(123,124)(128,133)(129,132)
(130,131)(135,140)(136,139)(137,138)(142,147)(143,146)(144,145)(149,154)
(150,153)(151,152)(156,161)(157,160)(158,159)(163,168)(164,167)(165,166)
(170,175)(171,174)(172,173)(177,182)(178,181)(179,180)(184,189)(185,188)
(186,187)(191,196)(192,195)(193,194)(198,203)(199,202)(200,201)(205,210)
(206,209)(207,208)(212,217)(213,216)(214,215)(219,224)(220,223)(221,222)
(226,231)(227,230)(228,229)(233,238)(234,237)(235,236)(240,245)(241,244)
(242,243)(247,252)(248,251)(249,250)(254,259)(255,258)(256,257)(261,266)
(262,265)(263,264)(268,273)(269,272)(270,271)(275,280)(276,279)(277,278)
(282,287)(283,286)(284,285)(289,294)(290,293)(291,292);;
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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*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, 43)(  9, 49)( 10, 48)( 11, 47)
( 12, 46)( 13, 45)( 14, 44)( 15, 36)( 16, 42)( 17, 41)( 18, 40)( 19, 39)
( 20, 38)( 21, 37)( 22, 29)( 23, 35)( 24, 34)( 25, 33)( 26, 32)( 27, 31)
( 28, 30)( 50, 99)( 51,105)( 52,104)( 53,103)( 54,102)( 55,101)( 56,100)
( 57,141)( 58,147)( 59,146)( 60,145)( 61,144)( 62,143)( 63,142)( 64,134)
( 65,140)( 66,139)( 67,138)( 68,137)( 69,136)( 70,135)( 71,127)( 72,133)
( 73,132)( 74,131)( 75,130)( 76,129)( 77,128)( 78,120)( 79,126)( 80,125)
( 81,124)( 82,123)( 83,122)( 84,121)( 85,113)( 86,119)( 87,118)( 88,117)
( 89,116)( 90,115)( 91,114)( 92,106)( 93,112)( 94,111)( 95,110)( 96,109)
( 97,108)( 98,107)(149,154)(150,153)(151,152)(155,190)(156,196)(157,195)
(158,194)(159,193)(160,192)(161,191)(162,183)(163,189)(164,188)(165,187)
(166,186)(167,185)(168,184)(169,176)(170,182)(171,181)(172,180)(173,179)
(174,178)(175,177)(197,246)(198,252)(199,251)(200,250)(201,249)(202,248)
(203,247)(204,288)(205,294)(206,293)(207,292)(208,291)(209,290)(210,289)
(211,281)(212,287)(213,286)(214,285)(215,284)(216,283)(217,282)(218,274)
(219,280)(220,279)(221,278)(222,277)(223,276)(224,275)(225,267)(226,273)
(227,272)(228,271)(229,270)(230,269)(231,268)(232,260)(233,266)(234,265)
(235,264)(236,263)(237,262)(238,261)(239,253)(240,259)(241,258)(242,257)
(243,256)(244,255)(245,254);
s1 := Sym(294)!(  1,205)(  2,204)(  3,210)(  4,209)(  5,208)(  6,207)(  7,206)
(  8,198)(  9,197)( 10,203)( 11,202)( 12,201)( 13,200)( 14,199)( 15,240)
( 16,239)( 17,245)( 18,244)( 19,243)( 20,242)( 21,241)( 22,233)( 23,232)
( 24,238)( 25,237)( 26,236)( 27,235)( 28,234)( 29,226)( 30,225)( 31,231)
( 32,230)( 33,229)( 34,228)( 35,227)( 36,219)( 37,218)( 38,224)( 39,223)
( 40,222)( 41,221)( 42,220)( 43,212)( 44,211)( 45,217)( 46,216)( 47,215)
( 48,214)( 49,213)( 50,156)( 51,155)( 52,161)( 53,160)( 54,159)( 55,158)
( 56,157)( 57,149)( 58,148)( 59,154)( 60,153)( 61,152)( 62,151)( 63,150)
( 64,191)( 65,190)( 66,196)( 67,195)( 68,194)( 69,193)( 70,192)( 71,184)
( 72,183)( 73,189)( 74,188)( 75,187)( 76,186)( 77,185)( 78,177)( 79,176)
( 80,182)( 81,181)( 82,180)( 83,179)( 84,178)( 85,170)( 86,169)( 87,175)
( 88,174)( 89,173)( 90,172)( 91,171)( 92,163)( 93,162)( 94,168)( 95,167)
( 96,166)( 97,165)( 98,164)( 99,254)(100,253)(101,259)(102,258)(103,257)
(104,256)(105,255)(106,247)(107,246)(108,252)(109,251)(110,250)(111,249)
(112,248)(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);
s2 := Sym(294)!(  2,  7)(  3,  6)(  4,  5)(  9, 14)( 10, 13)( 11, 12)( 16, 21)
( 17, 20)( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 30, 35)( 31, 34)( 32, 33)
( 37, 42)( 38, 41)( 39, 40)( 44, 49)( 45, 48)( 46, 47)( 51, 56)( 52, 55)
( 53, 54)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)( 72, 77)
( 73, 76)( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 86, 91)( 87, 90)( 88, 89)
( 93, 98)( 94, 97)( 95, 96)(100,105)(101,104)(102,103)(107,112)(108,111)
(109,110)(114,119)(115,118)(116,117)(121,126)(122,125)(123,124)(128,133)
(129,132)(130,131)(135,140)(136,139)(137,138)(142,147)(143,146)(144,145)
(149,154)(150,153)(151,152)(156,161)(157,160)(158,159)(163,168)(164,167)
(165,166)(170,175)(171,174)(172,173)(177,182)(178,181)(179,180)(184,189)
(185,188)(186,187)(191,196)(192,195)(193,194)(198,203)(199,202)(200,201)
(205,210)(206,209)(207,208)(212,217)(213,216)(214,215)(219,224)(220,223)
(221,222)(226,231)(227,230)(228,229)(233,238)(234,237)(235,236)(240,245)
(241,244)(242,243)(247,252)(248,251)(249,250)(254,259)(255,258)(256,257)
(261,266)(262,265)(263,264)(268,273)(269,272)(270,271)(275,280)(276,279)
(277,278)(282,287)(283,286)(284,285)(289,294)(290,293)(291,292);
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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*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