Polytope of Type {6,142}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,142}*1704
Also Known As : {6,142|2}. if this polytope has another name.
Group : SmallGroup(1704,34)
Rank : 3
Schlafli Type : {6,142}
Number of vertices, edges, etc : 6, 426, 142
Order of s₀s₁s₂ : 426
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 : {2,142}*568
   6-fold quotients : {2,71}*284
   71-fold quotients : {6,2}*24
   142-fold quotients : {3,2}*12
   213-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 72,143)( 73,144)( 74,145)( 75,146)( 76,147)( 77,148)( 78,149)( 79,150)
( 80,151)( 81,152)( 82,153)( 83,154)( 84,155)( 85,156)( 86,157)( 87,158)
( 88,159)( 89,160)( 90,161)( 91,162)( 92,163)( 93,164)( 94,165)( 95,166)
( 96,167)( 97,168)( 98,169)( 99,170)(100,171)(101,172)(102,173)(103,174)
(104,175)(105,176)(106,177)(107,178)(108,179)(109,180)(110,181)(111,182)
(112,183)(113,184)(114,185)(115,186)(116,187)(117,188)(118,189)(119,190)
(120,191)(121,192)(122,193)(123,194)(124,195)(125,196)(126,197)(127,198)
(128,199)(129,200)(130,201)(131,202)(132,203)(133,204)(134,205)(135,206)
(136,207)(137,208)(138,209)(139,210)(140,211)(141,212)(142,213)(285,356)
(286,357)(287,358)(288,359)(289,360)(290,361)(291,362)(292,363)(293,364)
(294,365)(295,366)(296,367)(297,368)(298,369)(299,370)(300,371)(301,372)
(302,373)(303,374)(304,375)(305,376)(306,377)(307,378)(308,379)(309,380)
(310,381)(311,382)(312,383)(313,384)(314,385)(315,386)(316,387)(317,388)
(318,389)(319,390)(320,391)(321,392)(322,393)(323,394)(324,395)(325,396)
(326,397)(327,398)(328,399)(329,400)(330,401)(331,402)(332,403)(333,404)
(334,405)(335,406)(336,407)(337,408)(338,409)(339,410)(340,411)(341,412)
(342,413)(343,414)(344,415)(345,416)(346,417)(347,418)(348,419)(349,420)
(350,421)(351,422)(352,423)(353,424)(354,425)(355,426);;
s1 := (  1, 72)(  2,142)(  3,141)(  4,140)(  5,139)(  6,138)(  7,137)(  8,136)
(  9,135)( 10,134)( 11,133)( 12,132)( 13,131)( 14,130)( 15,129)( 16,128)
( 17,127)( 18,126)( 19,125)( 20,124)( 21,123)( 22,122)( 23,121)( 24,120)
( 25,119)( 26,118)( 27,117)( 28,116)( 29,115)( 30,114)( 31,113)( 32,112)
( 33,111)( 34,110)( 35,109)( 36,108)( 37,107)( 38,106)( 39,105)( 40,104)
( 41,103)( 42,102)( 43,101)( 44,100)( 45, 99)( 46, 98)( 47, 97)( 48, 96)
( 49, 95)( 50, 94)( 51, 93)( 52, 92)( 53, 91)( 54, 90)( 55, 89)( 56, 88)
( 57, 87)( 58, 86)( 59, 85)( 60, 84)( 61, 83)( 62, 82)( 63, 81)( 64, 80)
( 65, 79)( 66, 78)( 67, 77)( 68, 76)( 69, 75)( 70, 74)( 71, 73)(144,213)
(145,212)(146,211)(147,210)(148,209)(149,208)(150,207)(151,206)(152,205)
(153,204)(154,203)(155,202)(156,201)(157,200)(158,199)(159,198)(160,197)
(161,196)(162,195)(163,194)(164,193)(165,192)(166,191)(167,190)(168,189)
(169,188)(170,187)(171,186)(172,185)(173,184)(174,183)(175,182)(176,181)
(177,180)(178,179)(214,285)(215,355)(216,354)(217,353)(218,352)(219,351)
(220,350)(221,349)(222,348)(223,347)(224,346)(225,345)(226,344)(227,343)
(228,342)(229,341)(230,340)(231,339)(232,338)(233,337)(234,336)(235,335)
(236,334)(237,333)(238,332)(239,331)(240,330)(241,329)(242,328)(243,327)
(244,326)(245,325)(246,324)(247,323)(248,322)(249,321)(250,320)(251,319)
(252,318)(253,317)(254,316)(255,315)(256,314)(257,313)(258,312)(259,311)
(260,310)(261,309)(262,308)(263,307)(264,306)(265,305)(266,304)(267,303)
(268,302)(269,301)(270,300)(271,299)(272,298)(273,297)(274,296)(275,295)
(276,294)(277,293)(278,292)(279,291)(280,290)(281,289)(282,288)(283,287)
(284,286)(357,426)(358,425)(359,424)(360,423)(361,422)(362,421)(363,420)
(364,419)(365,418)(366,417)(367,416)(368,415)(369,414)(370,413)(371,412)
(372,411)(373,410)(374,409)(375,408)(376,407)(377,406)(378,405)(379,404)
(380,403)(381,402)(382,401)(383,400)(384,399)(385,398)(386,397)(387,396)
(388,395)(389,394)(390,393)(391,392);;
s2 := (  1,215)(  2,214)(  3,284)(  4,283)(  5,282)(  6,281)(  7,280)(  8,279)
(  9,278)( 10,277)( 11,276)( 12,275)( 13,274)( 14,273)( 15,272)( 16,271)
( 17,270)( 18,269)( 19,268)( 20,267)( 21,266)( 22,265)( 23,264)( 24,263)
( 25,262)( 26,261)( 27,260)( 28,259)( 29,258)( 30,257)( 31,256)( 32,255)
( 33,254)( 34,253)( 35,252)( 36,251)( 37,250)( 38,249)( 39,248)( 40,247)
( 41,246)( 42,245)( 43,244)( 44,243)( 45,242)( 46,241)( 47,240)( 48,239)
( 49,238)( 50,237)( 51,236)( 52,235)( 53,234)( 54,233)( 55,232)( 56,231)
( 57,230)( 58,229)( 59,228)( 60,227)( 61,226)( 62,225)( 63,224)( 64,223)
( 65,222)( 66,221)( 67,220)( 68,219)( 69,218)( 70,217)( 71,216)( 72,286)
( 73,285)( 74,355)( 75,354)( 76,353)( 77,352)( 78,351)( 79,350)( 80,349)
( 81,348)( 82,347)( 83,346)( 84,345)( 85,344)( 86,343)( 87,342)( 88,341)
( 89,340)( 90,339)( 91,338)( 92,337)( 93,336)( 94,335)( 95,334)( 96,333)
( 97,332)( 98,331)( 99,330)(100,329)(101,328)(102,327)(103,326)(104,325)
(105,324)(106,323)(107,322)(108,321)(109,320)(110,319)(111,318)(112,317)
(113,316)(114,315)(115,314)(116,313)(117,312)(118,311)(119,310)(120,309)
(121,308)(122,307)(123,306)(124,305)(125,304)(126,303)(127,302)(128,301)
(129,300)(130,299)(131,298)(132,297)(133,296)(134,295)(135,294)(136,293)
(137,292)(138,291)(139,290)(140,289)(141,288)(142,287)(143,357)(144,356)
(145,426)(146,425)(147,424)(148,423)(149,422)(150,421)(151,420)(152,419)
(153,418)(154,417)(155,416)(156,415)(157,414)(158,413)(159,412)(160,411)
(161,410)(162,409)(163,408)(164,407)(165,406)(166,405)(167,404)(168,403)
(169,402)(170,401)(171,400)(172,399)(173,398)(174,397)(175,396)(176,395)
(177,394)(178,393)(179,392)(180,391)(181,390)(182,389)(183,388)(184,387)
(185,386)(186,385)(187,384)(188,383)(189,382)(190,381)(191,380)(192,379)
(193,378)(194,377)(195,376)(196,375)(197,374)(198,373)(199,372)(200,371)
(201,370)(202,369)(203,368)(204,367)(205,366)(206,365)(207,364)(208,363)
(209,362)(210,361)(211,360)(212,359)(213,358);;
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, 
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(426)!( 72,143)( 73,144)( 74,145)( 75,146)( 76,147)( 77,148)( 78,149)
( 79,150)( 80,151)( 81,152)( 82,153)( 83,154)( 84,155)( 85,156)( 86,157)
( 87,158)( 88,159)( 89,160)( 90,161)( 91,162)( 92,163)( 93,164)( 94,165)
( 95,166)( 96,167)( 97,168)( 98,169)( 99,170)(100,171)(101,172)(102,173)
(103,174)(104,175)(105,176)(106,177)(107,178)(108,179)(109,180)(110,181)
(111,182)(112,183)(113,184)(114,185)(115,186)(116,187)(117,188)(118,189)
(119,190)(120,191)(121,192)(122,193)(123,194)(124,195)(125,196)(126,197)
(127,198)(128,199)(129,200)(130,201)(131,202)(132,203)(133,204)(134,205)
(135,206)(136,207)(137,208)(138,209)(139,210)(140,211)(141,212)(142,213)
(285,356)(286,357)(287,358)(288,359)(289,360)(290,361)(291,362)(292,363)
(293,364)(294,365)(295,366)(296,367)(297,368)(298,369)(299,370)(300,371)
(301,372)(302,373)(303,374)(304,375)(305,376)(306,377)(307,378)(308,379)
(309,380)(310,381)(311,382)(312,383)(313,384)(314,385)(315,386)(316,387)
(317,388)(318,389)(319,390)(320,391)(321,392)(322,393)(323,394)(324,395)
(325,396)(326,397)(327,398)(328,399)(329,400)(330,401)(331,402)(332,403)
(333,404)(334,405)(335,406)(336,407)(337,408)(338,409)(339,410)(340,411)
(341,412)(342,413)(343,414)(344,415)(345,416)(346,417)(347,418)(348,419)
(349,420)(350,421)(351,422)(352,423)(353,424)(354,425)(355,426);
s1 := Sym(426)!(  1, 72)(  2,142)(  3,141)(  4,140)(  5,139)(  6,138)(  7,137)
(  8,136)(  9,135)( 10,134)( 11,133)( 12,132)( 13,131)( 14,130)( 15,129)
( 16,128)( 17,127)( 18,126)( 19,125)( 20,124)( 21,123)( 22,122)( 23,121)
( 24,120)( 25,119)( 26,118)( 27,117)( 28,116)( 29,115)( 30,114)( 31,113)
( 32,112)( 33,111)( 34,110)( 35,109)( 36,108)( 37,107)( 38,106)( 39,105)
( 40,104)( 41,103)( 42,102)( 43,101)( 44,100)( 45, 99)( 46, 98)( 47, 97)
( 48, 96)( 49, 95)( 50, 94)( 51, 93)( 52, 92)( 53, 91)( 54, 90)( 55, 89)
( 56, 88)( 57, 87)( 58, 86)( 59, 85)( 60, 84)( 61, 83)( 62, 82)( 63, 81)
( 64, 80)( 65, 79)( 66, 78)( 67, 77)( 68, 76)( 69, 75)( 70, 74)( 71, 73)
(144,213)(145,212)(146,211)(147,210)(148,209)(149,208)(150,207)(151,206)
(152,205)(153,204)(154,203)(155,202)(156,201)(157,200)(158,199)(159,198)
(160,197)(161,196)(162,195)(163,194)(164,193)(165,192)(166,191)(167,190)
(168,189)(169,188)(170,187)(171,186)(172,185)(173,184)(174,183)(175,182)
(176,181)(177,180)(178,179)(214,285)(215,355)(216,354)(217,353)(218,352)
(219,351)(220,350)(221,349)(222,348)(223,347)(224,346)(225,345)(226,344)
(227,343)(228,342)(229,341)(230,340)(231,339)(232,338)(233,337)(234,336)
(235,335)(236,334)(237,333)(238,332)(239,331)(240,330)(241,329)(242,328)
(243,327)(244,326)(245,325)(246,324)(247,323)(248,322)(249,321)(250,320)
(251,319)(252,318)(253,317)(254,316)(255,315)(256,314)(257,313)(258,312)
(259,311)(260,310)(261,309)(262,308)(263,307)(264,306)(265,305)(266,304)
(267,303)(268,302)(269,301)(270,300)(271,299)(272,298)(273,297)(274,296)
(275,295)(276,294)(277,293)(278,292)(279,291)(280,290)(281,289)(282,288)
(283,287)(284,286)(357,426)(358,425)(359,424)(360,423)(361,422)(362,421)
(363,420)(364,419)(365,418)(366,417)(367,416)(368,415)(369,414)(370,413)
(371,412)(372,411)(373,410)(374,409)(375,408)(376,407)(377,406)(378,405)
(379,404)(380,403)(381,402)(382,401)(383,400)(384,399)(385,398)(386,397)
(387,396)(388,395)(389,394)(390,393)(391,392);
s2 := Sym(426)!(  1,215)(  2,214)(  3,284)(  4,283)(  5,282)(  6,281)(  7,280)
(  8,279)(  9,278)( 10,277)( 11,276)( 12,275)( 13,274)( 14,273)( 15,272)
( 16,271)( 17,270)( 18,269)( 19,268)( 20,267)( 21,266)( 22,265)( 23,264)
( 24,263)( 25,262)( 26,261)( 27,260)( 28,259)( 29,258)( 30,257)( 31,256)
( 32,255)( 33,254)( 34,253)( 35,252)( 36,251)( 37,250)( 38,249)( 39,248)
( 40,247)( 41,246)( 42,245)( 43,244)( 44,243)( 45,242)( 46,241)( 47,240)
( 48,239)( 49,238)( 50,237)( 51,236)( 52,235)( 53,234)( 54,233)( 55,232)
( 56,231)( 57,230)( 58,229)( 59,228)( 60,227)( 61,226)( 62,225)( 63,224)
( 64,223)( 65,222)( 66,221)( 67,220)( 68,219)( 69,218)( 70,217)( 71,216)
( 72,286)( 73,285)( 74,355)( 75,354)( 76,353)( 77,352)( 78,351)( 79,350)
( 80,349)( 81,348)( 82,347)( 83,346)( 84,345)( 85,344)( 86,343)( 87,342)
( 88,341)( 89,340)( 90,339)( 91,338)( 92,337)( 93,336)( 94,335)( 95,334)
( 96,333)( 97,332)( 98,331)( 99,330)(100,329)(101,328)(102,327)(103,326)
(104,325)(105,324)(106,323)(107,322)(108,321)(109,320)(110,319)(111,318)
(112,317)(113,316)(114,315)(115,314)(116,313)(117,312)(118,311)(119,310)
(120,309)(121,308)(122,307)(123,306)(124,305)(125,304)(126,303)(127,302)
(128,301)(129,300)(130,299)(131,298)(132,297)(133,296)(134,295)(135,294)
(136,293)(137,292)(138,291)(139,290)(140,289)(141,288)(142,287)(143,357)
(144,356)(145,426)(146,425)(147,424)(148,423)(149,422)(150,421)(151,420)
(152,419)(153,418)(154,417)(155,416)(156,415)(157,414)(158,413)(159,412)
(160,411)(161,410)(162,409)(163,408)(164,407)(165,406)(166,405)(167,404)
(168,403)(169,402)(170,401)(171,400)(172,399)(173,398)(174,397)(175,396)
(176,395)(177,394)(178,393)(179,392)(180,391)(181,390)(182,389)(183,388)
(184,387)(185,386)(186,385)(187,384)(188,383)(189,382)(190,381)(191,380)
(192,379)(193,378)(194,377)(195,376)(196,375)(197,374)(198,373)(199,372)
(200,371)(201,370)(202,369)(203,368)(204,367)(205,366)(206,365)(207,364)
(208,363)(209,362)(210,361)(211,360)(212,359)(213,358);
poly := sub<Sym(426)|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, 
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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