Polytope of Type {99,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {99,6}*1188
if this polytope has a name.
Group : SmallGroup(1188,39)
Rank : 3
Schlafli Type : {99,6}
Number of vertices, edges, etc : 99, 297, 6
Order of s₀s₁s₂ : 198
Order of s₀s₁s₂s₁ : 6
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) :
   3-fold quotients : {99,2}*396, {33,6}*396
   9-fold quotients : {33,2}*132
   11-fold quotients : {9,6}*108
   27-fold quotients : {11,2}*44
   33-fold quotients : {9,2}*36, {3,6}*36
   99-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,  3)(  4, 31)(  5, 33)(  6, 32)(  7, 28)(  8, 30)(  9, 29)( 10, 25)
( 11, 27)( 12, 26)( 13, 22)( 14, 24)( 15, 23)( 16, 19)( 17, 21)( 18, 20)
( 34, 67)( 35, 69)( 36, 68)( 37, 97)( 38, 99)( 39, 98)( 40, 94)( 41, 96)
( 42, 95)( 43, 91)( 44, 93)( 45, 92)( 46, 88)( 47, 90)( 48, 89)( 49, 85)
( 50, 87)( 51, 86)( 52, 82)( 53, 84)( 54, 83)( 55, 79)( 56, 81)( 57, 80)
( 58, 76)( 59, 78)( 60, 77)( 61, 73)( 62, 75)( 63, 74)( 64, 70)( 65, 72)
( 66, 71)(100,200)(101,199)(102,201)(103,230)(104,229)(105,231)(106,227)
(107,226)(108,228)(109,224)(110,223)(111,225)(112,221)(113,220)(114,222)
(115,218)(116,217)(117,219)(118,215)(119,214)(120,216)(121,212)(122,211)
(123,213)(124,209)(125,208)(126,210)(127,206)(128,205)(129,207)(130,203)
(131,202)(132,204)(133,266)(134,265)(135,267)(136,296)(137,295)(138,297)
(139,293)(140,292)(141,294)(142,290)(143,289)(144,291)(145,287)(146,286)
(147,288)(148,284)(149,283)(150,285)(151,281)(152,280)(153,282)(154,278)
(155,277)(156,279)(157,275)(158,274)(159,276)(160,272)(161,271)(162,273)
(163,269)(164,268)(165,270)(166,233)(167,232)(168,234)(169,263)(170,262)
(171,264)(172,260)(173,259)(174,261)(175,257)(176,256)(177,258)(178,254)
(179,253)(180,255)(181,251)(182,250)(183,252)(184,248)(185,247)(186,249)
(187,245)(188,244)(189,246)(190,242)(191,241)(192,243)(193,239)(194,238)
(195,240)(196,236)(197,235)(198,237);;
s1 := (  1,136)(  2,138)(  3,137)(  4,133)(  5,135)(  6,134)(  7,163)(  8,165)
(  9,164)( 10,160)( 11,162)( 12,161)( 13,157)( 14,159)( 15,158)( 16,154)
( 17,156)( 18,155)( 19,151)( 20,153)( 21,152)( 22,148)( 23,150)( 24,149)
( 25,145)( 26,147)( 27,146)( 28,142)( 29,144)( 30,143)( 31,139)( 32,141)
( 33,140)( 34,103)( 35,105)( 36,104)( 37,100)( 38,102)( 39,101)( 40,130)
( 41,132)( 42,131)( 43,127)( 44,129)( 45,128)( 46,124)( 47,126)( 48,125)
( 49,121)( 50,123)( 51,122)( 52,118)( 53,120)( 54,119)( 55,115)( 56,117)
( 57,116)( 58,112)( 59,114)( 60,113)( 61,109)( 62,111)( 63,110)( 64,106)
( 65,108)( 66,107)( 67,169)( 68,171)( 69,170)( 70,166)( 71,168)( 72,167)
( 73,196)( 74,198)( 75,197)( 76,193)( 77,195)( 78,194)( 79,190)( 80,192)
( 81,191)( 82,187)( 83,189)( 84,188)( 85,184)( 86,186)( 87,185)( 88,181)
( 89,183)( 90,182)( 91,178)( 92,180)( 93,179)( 94,175)( 95,177)( 96,176)
( 97,172)( 98,174)( 99,173)(199,236)(200,235)(201,237)(202,233)(203,232)
(204,234)(205,263)(206,262)(207,264)(208,260)(209,259)(210,261)(211,257)
(212,256)(213,258)(214,254)(215,253)(216,255)(217,251)(218,250)(219,252)
(220,248)(221,247)(222,249)(223,245)(224,244)(225,246)(226,242)(227,241)
(228,243)(229,239)(230,238)(231,240)(265,269)(266,268)(267,270)(271,296)
(272,295)(273,297)(274,293)(275,292)(276,294)(277,290)(278,289)(279,291)
(280,287)(281,286)(282,288)(283,284);;
s2 := ( 34, 67)( 35, 68)( 36, 69)( 37, 70)( 38, 71)( 39, 72)( 40, 73)( 41, 74)
( 42, 75)( 43, 76)( 44, 77)( 45, 78)( 46, 79)( 47, 80)( 48, 81)( 49, 82)
( 50, 83)( 51, 84)( 52, 85)( 53, 86)( 54, 87)( 55, 88)( 56, 89)( 57, 90)
( 58, 91)( 59, 92)( 60, 93)( 61, 94)( 62, 95)( 63, 96)( 64, 97)( 65, 98)
( 66, 99)(133,166)(134,167)(135,168)(136,169)(137,170)(138,171)(139,172)
(140,173)(141,174)(142,175)(143,176)(144,177)(145,178)(146,179)(147,180)
(148,181)(149,182)(150,183)(151,184)(152,185)(153,186)(154,187)(155,188)
(156,189)(157,190)(158,191)(159,192)(160,193)(161,194)(162,195)(163,196)
(164,197)(165,198)(232,265)(233,266)(234,267)(235,268)(236,269)(237,270)
(238,271)(239,272)(240,273)(241,274)(242,275)(243,276)(244,277)(245,278)
(246,279)(247,280)(248,281)(249,282)(250,283)(251,284)(252,285)(253,286)
(254,287)(255,288)(256,289)(257,290)(258,291)(259,292)(260,293)(261,294)
(262,295)(263,296)(264,297);;
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*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(297)!(  2,  3)(  4, 31)(  5, 33)(  6, 32)(  7, 28)(  8, 30)(  9, 29)
( 10, 25)( 11, 27)( 12, 26)( 13, 22)( 14, 24)( 15, 23)( 16, 19)( 17, 21)
( 18, 20)( 34, 67)( 35, 69)( 36, 68)( 37, 97)( 38, 99)( 39, 98)( 40, 94)
( 41, 96)( 42, 95)( 43, 91)( 44, 93)( 45, 92)( 46, 88)( 47, 90)( 48, 89)
( 49, 85)( 50, 87)( 51, 86)( 52, 82)( 53, 84)( 54, 83)( 55, 79)( 56, 81)
( 57, 80)( 58, 76)( 59, 78)( 60, 77)( 61, 73)( 62, 75)( 63, 74)( 64, 70)
( 65, 72)( 66, 71)(100,200)(101,199)(102,201)(103,230)(104,229)(105,231)
(106,227)(107,226)(108,228)(109,224)(110,223)(111,225)(112,221)(113,220)
(114,222)(115,218)(116,217)(117,219)(118,215)(119,214)(120,216)(121,212)
(122,211)(123,213)(124,209)(125,208)(126,210)(127,206)(128,205)(129,207)
(130,203)(131,202)(132,204)(133,266)(134,265)(135,267)(136,296)(137,295)
(138,297)(139,293)(140,292)(141,294)(142,290)(143,289)(144,291)(145,287)
(146,286)(147,288)(148,284)(149,283)(150,285)(151,281)(152,280)(153,282)
(154,278)(155,277)(156,279)(157,275)(158,274)(159,276)(160,272)(161,271)
(162,273)(163,269)(164,268)(165,270)(166,233)(167,232)(168,234)(169,263)
(170,262)(171,264)(172,260)(173,259)(174,261)(175,257)(176,256)(177,258)
(178,254)(179,253)(180,255)(181,251)(182,250)(183,252)(184,248)(185,247)
(186,249)(187,245)(188,244)(189,246)(190,242)(191,241)(192,243)(193,239)
(194,238)(195,240)(196,236)(197,235)(198,237);
s1 := Sym(297)!(  1,136)(  2,138)(  3,137)(  4,133)(  5,135)(  6,134)(  7,163)
(  8,165)(  9,164)( 10,160)( 11,162)( 12,161)( 13,157)( 14,159)( 15,158)
( 16,154)( 17,156)( 18,155)( 19,151)( 20,153)( 21,152)( 22,148)( 23,150)
( 24,149)( 25,145)( 26,147)( 27,146)( 28,142)( 29,144)( 30,143)( 31,139)
( 32,141)( 33,140)( 34,103)( 35,105)( 36,104)( 37,100)( 38,102)( 39,101)
( 40,130)( 41,132)( 42,131)( 43,127)( 44,129)( 45,128)( 46,124)( 47,126)
( 48,125)( 49,121)( 50,123)( 51,122)( 52,118)( 53,120)( 54,119)( 55,115)
( 56,117)( 57,116)( 58,112)( 59,114)( 60,113)( 61,109)( 62,111)( 63,110)
( 64,106)( 65,108)( 66,107)( 67,169)( 68,171)( 69,170)( 70,166)( 71,168)
( 72,167)( 73,196)( 74,198)( 75,197)( 76,193)( 77,195)( 78,194)( 79,190)
( 80,192)( 81,191)( 82,187)( 83,189)( 84,188)( 85,184)( 86,186)( 87,185)
( 88,181)( 89,183)( 90,182)( 91,178)( 92,180)( 93,179)( 94,175)( 95,177)
( 96,176)( 97,172)( 98,174)( 99,173)(199,236)(200,235)(201,237)(202,233)
(203,232)(204,234)(205,263)(206,262)(207,264)(208,260)(209,259)(210,261)
(211,257)(212,256)(213,258)(214,254)(215,253)(216,255)(217,251)(218,250)
(219,252)(220,248)(221,247)(222,249)(223,245)(224,244)(225,246)(226,242)
(227,241)(228,243)(229,239)(230,238)(231,240)(265,269)(266,268)(267,270)
(271,296)(272,295)(273,297)(274,293)(275,292)(276,294)(277,290)(278,289)
(279,291)(280,287)(281,286)(282,288)(283,284);
s2 := Sym(297)!( 34, 67)( 35, 68)( 36, 69)( 37, 70)( 38, 71)( 39, 72)( 40, 73)
( 41, 74)( 42, 75)( 43, 76)( 44, 77)( 45, 78)( 46, 79)( 47, 80)( 48, 81)
( 49, 82)( 50, 83)( 51, 84)( 52, 85)( 53, 86)( 54, 87)( 55, 88)( 56, 89)
( 57, 90)( 58, 91)( 59, 92)( 60, 93)( 61, 94)( 62, 95)( 63, 96)( 64, 97)
( 65, 98)( 66, 99)(133,166)(134,167)(135,168)(136,169)(137,170)(138,171)
(139,172)(140,173)(141,174)(142,175)(143,176)(144,177)(145,178)(146,179)
(147,180)(148,181)(149,182)(150,183)(151,184)(152,185)(153,186)(154,187)
(155,188)(156,189)(157,190)(158,191)(159,192)(160,193)(161,194)(162,195)
(163,196)(164,197)(165,198)(232,265)(233,266)(234,267)(235,268)(236,269)
(237,270)(238,271)(239,272)(240,273)(241,274)(242,275)(243,276)(244,277)
(245,278)(246,279)(247,280)(248,281)(249,282)(250,283)(251,284)(252,285)
(253,286)(254,287)(255,288)(256,289)(257,290)(258,291)(259,292)(260,293)
(261,294)(262,295)(263,296)(264,297);
poly := sub<Sym(297)|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*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope