Polytope of Type {6,99}

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

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