Polytope of Type {14,6}

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