Polytope of Type {106,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {106,6}*1272
Also Known As : {106,6|2}. if this polytope has another name.
Group : SmallGroup(1272,39)
Rank : 3
Schlafli Type : {106,6}
Number of vertices, edges, etc : 106, 318, 6
Order of s₀s₁s₂ : 318
Order of s₀s₁s₂s₁ : 2
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 : {106,2}*424
   6-fold quotients : {53,2}*212
   53-fold quotients : {2,6}*24
   106-fold quotients : {2,3}*12
   159-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 53)(  3, 52)(  4, 51)(  5, 50)(  6, 49)(  7, 48)(  8, 47)(  9, 46)
( 10, 45)( 11, 44)( 12, 43)( 13, 42)( 14, 41)( 15, 40)( 16, 39)( 17, 38)
( 18, 37)( 19, 36)( 20, 35)( 21, 34)( 22, 33)( 23, 32)( 24, 31)( 25, 30)
( 26, 29)( 27, 28)( 55,106)( 56,105)( 57,104)( 58,103)( 59,102)( 60,101)
( 61,100)( 62, 99)( 63, 98)( 64, 97)( 65, 96)( 66, 95)( 67, 94)( 68, 93)
( 69, 92)( 70, 91)( 71, 90)( 72, 89)( 73, 88)( 74, 87)( 75, 86)( 76, 85)
( 77, 84)( 78, 83)( 79, 82)( 80, 81)(108,159)(109,158)(110,157)(111,156)
(112,155)(113,154)(114,153)(115,152)(116,151)(117,150)(118,149)(119,148)
(120,147)(121,146)(122,145)(123,144)(124,143)(125,142)(126,141)(127,140)
(128,139)(129,138)(130,137)(131,136)(132,135)(133,134)(161,212)(162,211)
(163,210)(164,209)(165,208)(166,207)(167,206)(168,205)(169,204)(170,203)
(171,202)(172,201)(173,200)(174,199)(175,198)(176,197)(177,196)(178,195)
(179,194)(180,193)(181,192)(182,191)(183,190)(184,189)(185,188)(186,187)
(214,265)(215,264)(216,263)(217,262)(218,261)(219,260)(220,259)(221,258)
(222,257)(223,256)(224,255)(225,254)(226,253)(227,252)(228,251)(229,250)
(230,249)(231,248)(232,247)(233,246)(234,245)(235,244)(236,243)(237,242)
(238,241)(239,240)(267,318)(268,317)(269,316)(270,315)(271,314)(272,313)
(273,312)(274,311)(275,310)(276,309)(277,308)(278,307)(279,306)(280,305)
(281,304)(282,303)(283,302)(284,301)(285,300)(286,299)(287,298)(288,297)
(289,296)(290,295)(291,294)(292,293);;
s1 := (  1,  2)(  3, 53)(  4, 52)(  5, 51)(  6, 50)(  7, 49)(  8, 48)(  9, 47)
( 10, 46)( 11, 45)( 12, 44)( 13, 43)( 14, 42)( 15, 41)( 16, 40)( 17, 39)
( 18, 38)( 19, 37)( 20, 36)( 21, 35)( 22, 34)( 23, 33)( 24, 32)( 25, 31)
( 26, 30)( 27, 29)( 54,108)( 55,107)( 56,159)( 57,158)( 58,157)( 59,156)
( 60,155)( 61,154)( 62,153)( 63,152)( 64,151)( 65,150)( 66,149)( 67,148)
( 68,147)( 69,146)( 70,145)( 71,144)( 72,143)( 73,142)( 74,141)( 75,140)
( 76,139)( 77,138)( 78,137)( 79,136)( 80,135)( 81,134)( 82,133)( 83,132)
( 84,131)( 85,130)( 86,129)( 87,128)( 88,127)( 89,126)( 90,125)( 91,124)
( 92,123)( 93,122)( 94,121)( 95,120)( 96,119)( 97,118)( 98,117)( 99,116)
(100,115)(101,114)(102,113)(103,112)(104,111)(105,110)(106,109)(160,161)
(162,212)(163,211)(164,210)(165,209)(166,208)(167,207)(168,206)(169,205)
(170,204)(171,203)(172,202)(173,201)(174,200)(175,199)(176,198)(177,197)
(178,196)(179,195)(180,194)(181,193)(182,192)(183,191)(184,190)(185,189)
(186,188)(213,267)(214,266)(215,318)(216,317)(217,316)(218,315)(219,314)
(220,313)(221,312)(222,311)(223,310)(224,309)(225,308)(226,307)(227,306)
(228,305)(229,304)(230,303)(231,302)(232,301)(233,300)(234,299)(235,298)
(236,297)(237,296)(238,295)(239,294)(240,293)(241,292)(242,291)(243,290)
(244,289)(245,288)(246,287)(247,286)(248,285)(249,284)(250,283)(251,282)
(252,281)(253,280)(254,279)(255,278)(256,277)(257,276)(258,275)(259,274)
(260,273)(261,272)(262,271)(263,270)(264,269)(265,268);;
s2 := (  1,213)(  2,214)(  3,215)(  4,216)(  5,217)(  6,218)(  7,219)(  8,220)
(  9,221)( 10,222)( 11,223)( 12,224)( 13,225)( 14,226)( 15,227)( 16,228)
( 17,229)( 18,230)( 19,231)( 20,232)( 21,233)( 22,234)( 23,235)( 24,236)
( 25,237)( 26,238)( 27,239)( 28,240)( 29,241)( 30,242)( 31,243)( 32,244)
( 33,245)( 34,246)( 35,247)( 36,248)( 37,249)( 38,250)( 39,251)( 40,252)
( 41,253)( 42,254)( 43,255)( 44,256)( 45,257)( 46,258)( 47,259)( 48,260)
( 49,261)( 50,262)( 51,263)( 52,264)( 53,265)( 54,160)( 55,161)( 56,162)
( 57,163)( 58,164)( 59,165)( 60,166)( 61,167)( 62,168)( 63,169)( 64,170)
( 65,171)( 66,172)( 67,173)( 68,174)( 69,175)( 70,176)( 71,177)( 72,178)
( 73,179)( 74,180)( 75,181)( 76,182)( 77,183)( 78,184)( 79,185)( 80,186)
( 81,187)( 82,188)( 83,189)( 84,190)( 85,191)( 86,192)( 87,193)( 88,194)
( 89,195)( 90,196)( 91,197)( 92,198)( 93,199)( 94,200)( 95,201)( 96,202)
( 97,203)( 98,204)( 99,205)(100,206)(101,207)(102,208)(103,209)(104,210)
(105,211)(106,212)(107,266)(108,267)(109,268)(110,269)(111,270)(112,271)
(113,272)(114,273)(115,274)(116,275)(117,276)(118,277)(119,278)(120,279)
(121,280)(122,281)(123,282)(124,283)(125,284)(126,285)(127,286)(128,287)
(129,288)(130,289)(131,290)(132,291)(133,292)(134,293)(135,294)(136,295)
(137,296)(138,297)(139,298)(140,299)(141,300)(142,301)(143,302)(144,303)
(145,304)(146,305)(147,306)(148,307)(149,308)(150,309)(151,310)(152,311)
(153,312)(154,313)(155,314)(156,315)(157,316)(158,317)(159,318);;
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*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(318)!(  2, 53)(  3, 52)(  4, 51)(  5, 50)(  6, 49)(  7, 48)(  8, 47)
(  9, 46)( 10, 45)( 11, 44)( 12, 43)( 13, 42)( 14, 41)( 15, 40)( 16, 39)
( 17, 38)( 18, 37)( 19, 36)( 20, 35)( 21, 34)( 22, 33)( 23, 32)( 24, 31)
( 25, 30)( 26, 29)( 27, 28)( 55,106)( 56,105)( 57,104)( 58,103)( 59,102)
( 60,101)( 61,100)( 62, 99)( 63, 98)( 64, 97)( 65, 96)( 66, 95)( 67, 94)
( 68, 93)( 69, 92)( 70, 91)( 71, 90)( 72, 89)( 73, 88)( 74, 87)( 75, 86)
( 76, 85)( 77, 84)( 78, 83)( 79, 82)( 80, 81)(108,159)(109,158)(110,157)
(111,156)(112,155)(113,154)(114,153)(115,152)(116,151)(117,150)(118,149)
(119,148)(120,147)(121,146)(122,145)(123,144)(124,143)(125,142)(126,141)
(127,140)(128,139)(129,138)(130,137)(131,136)(132,135)(133,134)(161,212)
(162,211)(163,210)(164,209)(165,208)(166,207)(167,206)(168,205)(169,204)
(170,203)(171,202)(172,201)(173,200)(174,199)(175,198)(176,197)(177,196)
(178,195)(179,194)(180,193)(181,192)(182,191)(183,190)(184,189)(185,188)
(186,187)(214,265)(215,264)(216,263)(217,262)(218,261)(219,260)(220,259)
(221,258)(222,257)(223,256)(224,255)(225,254)(226,253)(227,252)(228,251)
(229,250)(230,249)(231,248)(232,247)(233,246)(234,245)(235,244)(236,243)
(237,242)(238,241)(239,240)(267,318)(268,317)(269,316)(270,315)(271,314)
(272,313)(273,312)(274,311)(275,310)(276,309)(277,308)(278,307)(279,306)
(280,305)(281,304)(282,303)(283,302)(284,301)(285,300)(286,299)(287,298)
(288,297)(289,296)(290,295)(291,294)(292,293);
s1 := Sym(318)!(  1,  2)(  3, 53)(  4, 52)(  5, 51)(  6, 50)(  7, 49)(  8, 48)
(  9, 47)( 10, 46)( 11, 45)( 12, 44)( 13, 43)( 14, 42)( 15, 41)( 16, 40)
( 17, 39)( 18, 38)( 19, 37)( 20, 36)( 21, 35)( 22, 34)( 23, 33)( 24, 32)
( 25, 31)( 26, 30)( 27, 29)( 54,108)( 55,107)( 56,159)( 57,158)( 58,157)
( 59,156)( 60,155)( 61,154)( 62,153)( 63,152)( 64,151)( 65,150)( 66,149)
( 67,148)( 68,147)( 69,146)( 70,145)( 71,144)( 72,143)( 73,142)( 74,141)
( 75,140)( 76,139)( 77,138)( 78,137)( 79,136)( 80,135)( 81,134)( 82,133)
( 83,132)( 84,131)( 85,130)( 86,129)( 87,128)( 88,127)( 89,126)( 90,125)
( 91,124)( 92,123)( 93,122)( 94,121)( 95,120)( 96,119)( 97,118)( 98,117)
( 99,116)(100,115)(101,114)(102,113)(103,112)(104,111)(105,110)(106,109)
(160,161)(162,212)(163,211)(164,210)(165,209)(166,208)(167,207)(168,206)
(169,205)(170,204)(171,203)(172,202)(173,201)(174,200)(175,199)(176,198)
(177,197)(178,196)(179,195)(180,194)(181,193)(182,192)(183,191)(184,190)
(185,189)(186,188)(213,267)(214,266)(215,318)(216,317)(217,316)(218,315)
(219,314)(220,313)(221,312)(222,311)(223,310)(224,309)(225,308)(226,307)
(227,306)(228,305)(229,304)(230,303)(231,302)(232,301)(233,300)(234,299)
(235,298)(236,297)(237,296)(238,295)(239,294)(240,293)(241,292)(242,291)
(243,290)(244,289)(245,288)(246,287)(247,286)(248,285)(249,284)(250,283)
(251,282)(252,281)(253,280)(254,279)(255,278)(256,277)(257,276)(258,275)
(259,274)(260,273)(261,272)(262,271)(263,270)(264,269)(265,268);
s2 := Sym(318)!(  1,213)(  2,214)(  3,215)(  4,216)(  5,217)(  6,218)(  7,219)
(  8,220)(  9,221)( 10,222)( 11,223)( 12,224)( 13,225)( 14,226)( 15,227)
( 16,228)( 17,229)( 18,230)( 19,231)( 20,232)( 21,233)( 22,234)( 23,235)
( 24,236)( 25,237)( 26,238)( 27,239)( 28,240)( 29,241)( 30,242)( 31,243)
( 32,244)( 33,245)( 34,246)( 35,247)( 36,248)( 37,249)( 38,250)( 39,251)
( 40,252)( 41,253)( 42,254)( 43,255)( 44,256)( 45,257)( 46,258)( 47,259)
( 48,260)( 49,261)( 50,262)( 51,263)( 52,264)( 53,265)( 54,160)( 55,161)
( 56,162)( 57,163)( 58,164)( 59,165)( 60,166)( 61,167)( 62,168)( 63,169)
( 64,170)( 65,171)( 66,172)( 67,173)( 68,174)( 69,175)( 70,176)( 71,177)
( 72,178)( 73,179)( 74,180)( 75,181)( 76,182)( 77,183)( 78,184)( 79,185)
( 80,186)( 81,187)( 82,188)( 83,189)( 84,190)( 85,191)( 86,192)( 87,193)
( 88,194)( 89,195)( 90,196)( 91,197)( 92,198)( 93,199)( 94,200)( 95,201)
( 96,202)( 97,203)( 98,204)( 99,205)(100,206)(101,207)(102,208)(103,209)
(104,210)(105,211)(106,212)(107,266)(108,267)(109,268)(110,269)(111,270)
(112,271)(113,272)(114,273)(115,274)(116,275)(117,276)(118,277)(119,278)
(120,279)(121,280)(122,281)(123,282)(124,283)(125,284)(126,285)(127,286)
(128,287)(129,288)(130,289)(131,290)(132,291)(133,292)(134,293)(135,294)
(136,295)(137,296)(138,297)(139,298)(140,299)(141,300)(142,301)(143,302)
(144,303)(145,304)(146,305)(147,306)(148,307)(149,308)(150,309)(151,310)
(152,311)(153,312)(154,313)(155,314)(156,315)(157,316)(158,317)(159,318);
poly := sub<Sym(318)|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*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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