Polytope of Type {14,6}

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

References : None.
to this polytope