Polytope of Type {102,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {102,6}*1224c
if this polytope has a name.
Group : SmallGroup(1224,156)
Rank : 3
Schlafli Type : {102,6}
Number of vertices, edges, etc : 102, 306, 6
Order of s₀s₁s₂ : 102
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
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 : {51,6}*612
   3-fold quotients : {102,2}*408
   6-fold quotients : {51,2}*204
   9-fold quotients : {34,2}*136
   17-fold quotients : {6,6}*72c
   18-fold quotients : {17,2}*68
   34-fold quotients : {3,6}*36
   51-fold quotients : {6,2}*24
   102-fold quotients : {3,2}*12
   153-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope