Polytope of Type {6,102}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,102}*1224c
if this polytope has a name.
Group : SmallGroup(1224,156)
Rank : 3
Schlafli Type : {6,102}
Number of vertices, edges, etc : 6, 306, 102
Order of s₀s₁s₂ : 102
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) :
   2-fold quotients : {6,51}*612
   3-fold quotients : {2,102}*408
   6-fold quotients : {2,51}*204
   9-fold quotients : {2,34}*136
   17-fold quotients : {6,6}*72b
   18-fold quotients : {2,17}*68
   34-fold quotients : {6,3}*36
   51-fold quotients : {2,6}*24
   102-fold quotients : {2,3}*12
   153-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 52,103)( 53,104)( 54,105)( 55,106)( 56,107)( 57,108)( 58,109)( 59,110)
( 60,111)( 61,112)( 62,113)( 63,114)( 64,115)( 65,116)( 66,117)( 67,118)
( 68,119)( 69,120)( 70,121)( 71,122)( 72,123)( 73,124)( 74,125)( 75,126)
( 76,127)( 77,128)( 78,129)( 79,130)( 80,131)( 81,132)( 82,133)( 83,134)
( 84,135)( 85,136)( 86,137)( 87,138)( 88,139)( 89,140)( 90,141)( 91,142)
( 92,143)( 93,144)( 94,145)( 95,146)( 96,147)( 97,148)( 98,149)( 99,150)
(100,151)(101,152)(102,153)(205,256)(206,257)(207,258)(208,259)(209,260)
(210,261)(211,262)(212,263)(213,264)(214,265)(215,266)(216,267)(217,268)
(218,269)(219,270)(220,271)(221,272)(222,273)(223,274)(224,275)(225,276)
(226,277)(227,278)(228,279)(229,280)(230,281)(231,282)(232,283)(233,284)
(234,285)(235,286)(236,287)(237,288)(238,289)(239,290)(240,291)(241,292)
(242,293)(243,294)(244,295)(245,296)(246,297)(247,298)(248,299)(249,300)
(250,301)(251,302)(252,303)(253,304)(254,305)(255,306);;
s1 := (  1, 52)(  2, 68)(  3, 67)(  4, 66)(  5, 65)(  6, 64)(  7, 63)(  8, 62)
(  9, 61)( 10, 60)( 11, 59)( 12, 58)( 13, 57)( 14, 56)( 15, 55)( 16, 54)
( 17, 53)( 18, 86)( 19,102)( 20,101)( 21,100)( 22, 99)( 23, 98)( 24, 97)
( 25, 96)( 26, 95)( 27, 94)( 28, 93)( 29, 92)( 30, 91)( 31, 90)( 32, 89)
( 33, 88)( 34, 87)( 35, 69)( 36, 85)( 37, 84)( 38, 83)( 39, 82)( 40, 81)
( 41, 80)( 42, 79)( 43, 78)( 44, 77)( 45, 76)( 46, 75)( 47, 74)( 48, 73)
( 49, 72)( 50, 71)( 51, 70)(104,119)(105,118)(106,117)(107,116)(108,115)
(109,114)(110,113)(111,112)(120,137)(121,153)(122,152)(123,151)(124,150)
(125,149)(126,148)(127,147)(128,146)(129,145)(130,144)(131,143)(132,142)
(133,141)(134,140)(135,139)(136,138)(154,205)(155,221)(156,220)(157,219)
(158,218)(159,217)(160,216)(161,215)(162,214)(163,213)(164,212)(165,211)
(166,210)(167,209)(168,208)(169,207)(170,206)(171,239)(172,255)(173,254)
(174,253)(175,252)(176,251)(177,250)(178,249)(179,248)(180,247)(181,246)
(182,245)(183,244)(184,243)(185,242)(186,241)(187,240)(188,222)(189,238)
(190,237)(191,236)(192,235)(193,234)(194,233)(195,232)(196,231)(197,230)
(198,229)(199,228)(200,227)(201,226)(202,225)(203,224)(204,223)(257,272)
(258,271)(259,270)(260,269)(261,268)(262,267)(263,266)(264,265)(273,290)
(274,306)(275,305)(276,304)(277,303)(278,302)(279,301)(280,300)(281,299)
(282,298)(283,297)(284,296)(285,295)(286,294)(287,293)(288,292)(289,291);;
s2 := (  1,172)(  2,171)(  3,187)(  4,186)(  5,185)(  6,184)(  7,183)(  8,182)
(  9,181)( 10,180)( 11,179)( 12,178)( 13,177)( 14,176)( 15,175)( 16,174)
( 17,173)( 18,155)( 19,154)( 20,170)( 21,169)( 22,168)( 23,167)( 24,166)
( 25,165)( 26,164)( 27,163)( 28,162)( 29,161)( 30,160)( 31,159)( 32,158)
( 33,157)( 34,156)( 35,189)( 36,188)( 37,204)( 38,203)( 39,202)( 40,201)
( 41,200)( 42,199)( 43,198)( 44,197)( 45,196)( 46,195)( 47,194)( 48,193)
( 49,192)( 50,191)( 51,190)( 52,274)( 53,273)( 54,289)( 55,288)( 56,287)
( 57,286)( 58,285)( 59,284)( 60,283)( 61,282)( 62,281)( 63,280)( 64,279)
( 65,278)( 66,277)( 67,276)( 68,275)( 69,257)( 70,256)( 71,272)( 72,271)
( 73,270)( 74,269)( 75,268)( 76,267)( 77,266)( 78,265)( 79,264)( 80,263)
( 81,262)( 82,261)( 83,260)( 84,259)( 85,258)( 86,291)( 87,290)( 88,306)
( 89,305)( 90,304)( 91,303)( 92,302)( 93,301)( 94,300)( 95,299)( 96,298)
( 97,297)( 98,296)( 99,295)(100,294)(101,293)(102,292)(103,223)(104,222)
(105,238)(106,237)(107,236)(108,235)(109,234)(110,233)(111,232)(112,231)
(113,230)(114,229)(115,228)(116,227)(117,226)(118,225)(119,224)(120,206)
(121,205)(122,221)(123,220)(124,219)(125,218)(126,217)(127,216)(128,215)
(129,214)(130,213)(131,212)(132,211)(133,210)(134,209)(135,208)(136,207)
(137,240)(138,239)(139,255)(140,254)(141,253)(142,252)(143,251)(144,250)
(145,249)(146,248)(147,247)(148,246)(149,245)(150,244)(151,243)(152,242)
(153,241);;
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*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(306)!( 52,103)( 53,104)( 54,105)( 55,106)( 56,107)( 57,108)( 58,109)
( 59,110)( 60,111)( 61,112)( 62,113)( 63,114)( 64,115)( 65,116)( 66,117)
( 67,118)( 68,119)( 69,120)( 70,121)( 71,122)( 72,123)( 73,124)( 74,125)
( 75,126)( 76,127)( 77,128)( 78,129)( 79,130)( 80,131)( 81,132)( 82,133)
( 83,134)( 84,135)( 85,136)( 86,137)( 87,138)( 88,139)( 89,140)( 90,141)
( 91,142)( 92,143)( 93,144)( 94,145)( 95,146)( 96,147)( 97,148)( 98,149)
( 99,150)(100,151)(101,152)(102,153)(205,256)(206,257)(207,258)(208,259)
(209,260)(210,261)(211,262)(212,263)(213,264)(214,265)(215,266)(216,267)
(217,268)(218,269)(219,270)(220,271)(221,272)(222,273)(223,274)(224,275)
(225,276)(226,277)(227,278)(228,279)(229,280)(230,281)(231,282)(232,283)
(233,284)(234,285)(235,286)(236,287)(237,288)(238,289)(239,290)(240,291)
(241,292)(242,293)(243,294)(244,295)(245,296)(246,297)(247,298)(248,299)
(249,300)(250,301)(251,302)(252,303)(253,304)(254,305)(255,306);
s1 := Sym(306)!(  1, 52)(  2, 68)(  3, 67)(  4, 66)(  5, 65)(  6, 64)(  7, 63)
(  8, 62)(  9, 61)( 10, 60)( 11, 59)( 12, 58)( 13, 57)( 14, 56)( 15, 55)
( 16, 54)( 17, 53)( 18, 86)( 19,102)( 20,101)( 21,100)( 22, 99)( 23, 98)
( 24, 97)( 25, 96)( 26, 95)( 27, 94)( 28, 93)( 29, 92)( 30, 91)( 31, 90)
( 32, 89)( 33, 88)( 34, 87)( 35, 69)( 36, 85)( 37, 84)( 38, 83)( 39, 82)
( 40, 81)( 41, 80)( 42, 79)( 43, 78)( 44, 77)( 45, 76)( 46, 75)( 47, 74)
( 48, 73)( 49, 72)( 50, 71)( 51, 70)(104,119)(105,118)(106,117)(107,116)
(108,115)(109,114)(110,113)(111,112)(120,137)(121,153)(122,152)(123,151)
(124,150)(125,149)(126,148)(127,147)(128,146)(129,145)(130,144)(131,143)
(132,142)(133,141)(134,140)(135,139)(136,138)(154,205)(155,221)(156,220)
(157,219)(158,218)(159,217)(160,216)(161,215)(162,214)(163,213)(164,212)
(165,211)(166,210)(167,209)(168,208)(169,207)(170,206)(171,239)(172,255)
(173,254)(174,253)(175,252)(176,251)(177,250)(178,249)(179,248)(180,247)
(181,246)(182,245)(183,244)(184,243)(185,242)(186,241)(187,240)(188,222)
(189,238)(190,237)(191,236)(192,235)(193,234)(194,233)(195,232)(196,231)
(197,230)(198,229)(199,228)(200,227)(201,226)(202,225)(203,224)(204,223)
(257,272)(258,271)(259,270)(260,269)(261,268)(262,267)(263,266)(264,265)
(273,290)(274,306)(275,305)(276,304)(277,303)(278,302)(279,301)(280,300)
(281,299)(282,298)(283,297)(284,296)(285,295)(286,294)(287,293)(288,292)
(289,291);
s2 := Sym(306)!(  1,172)(  2,171)(  3,187)(  4,186)(  5,185)(  6,184)(  7,183)
(  8,182)(  9,181)( 10,180)( 11,179)( 12,178)( 13,177)( 14,176)( 15,175)
( 16,174)( 17,173)( 18,155)( 19,154)( 20,170)( 21,169)( 22,168)( 23,167)
( 24,166)( 25,165)( 26,164)( 27,163)( 28,162)( 29,161)( 30,160)( 31,159)
( 32,158)( 33,157)( 34,156)( 35,189)( 36,188)( 37,204)( 38,203)( 39,202)
( 40,201)( 41,200)( 42,199)( 43,198)( 44,197)( 45,196)( 46,195)( 47,194)
( 48,193)( 49,192)( 50,191)( 51,190)( 52,274)( 53,273)( 54,289)( 55,288)
( 56,287)( 57,286)( 58,285)( 59,284)( 60,283)( 61,282)( 62,281)( 63,280)
( 64,279)( 65,278)( 66,277)( 67,276)( 68,275)( 69,257)( 70,256)( 71,272)
( 72,271)( 73,270)( 74,269)( 75,268)( 76,267)( 77,266)( 78,265)( 79,264)
( 80,263)( 81,262)( 82,261)( 83,260)( 84,259)( 85,258)( 86,291)( 87,290)
( 88,306)( 89,305)( 90,304)( 91,303)( 92,302)( 93,301)( 94,300)( 95,299)
( 96,298)( 97,297)( 98,296)( 99,295)(100,294)(101,293)(102,292)(103,223)
(104,222)(105,238)(106,237)(107,236)(108,235)(109,234)(110,233)(111,232)
(112,231)(113,230)(114,229)(115,228)(116,227)(117,226)(118,225)(119,224)
(120,206)(121,205)(122,221)(123,220)(124,219)(125,218)(126,217)(127,216)
(128,215)(129,214)(130,213)(131,212)(132,211)(133,210)(134,209)(135,208)
(136,207)(137,240)(138,239)(139,255)(140,254)(141,253)(142,252)(143,251)
(144,250)(145,249)(146,248)(147,247)(148,246)(149,245)(150,244)(151,243)
(152,242)(153,241);
poly := sub<Sym(306)|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*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope