Polytope of Type {14,42}

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